Analyze and Solve Linear Equations Math B Honors
Module #1 Homework 2017-2018
Created in collaboration with Utah Middle School Math Project A University of Utah Partnership Project
San Dieguito Union High School District
1.1A Homework: Simplifying Expressions and Algebra Tiles* Name:
Period:
Directions: Name the property shown. 2. (
1.
(
3.
)
(
)
4.
5. Write four expressions that are equivalent to
)
(
)
(
)
( )
using the given property.
a. Commutative Property of Addition
b. Identity Property of Multiplication
c. Additive Inverse Property
d. Distributive Property
6. State if the statement is true or false. If false, explain why. a.
b. All fractions are rational numbers.
is an integer.
c.
is a rational number.
e. √
is a whole number.
d.
is a rational number.
f.
is a whole number.
Directions: A mistake was made when simplifying the expressions below. Identify and explain the mistake made. Simplify the expressions correctly. 7.
8.
simplifies to
(
) simplifies to
Explain mistake:
Correct answer:
Explain mistake:
Correct answer:
SDUHSD Math B Honors Module #1 – HOMEWORK 2017-2018
2
(
9.
10.
) simplifies to
Explain mistake:
Correct answer:
simplifies to
Explain mistake:
Correct answer:
11. A group of friends go to a movie on Friday night. Each friend purchases a movie ticket that costs $8, a small popcorn that costs $3.50, and a medium drink that costs $2.25. a. If f represents the number of friends that went to the movie, circle the expressions below that represent the total amount of money spent by the group. (
)
b. If 5 friends go to the movie, how much money will each person spend? How much money will the entire group spend?
Directions: Simplify the expression without using Algebra tiles. Evaluate for the given value. Show all of your work. 12. (
)
(
); Evaluate for
13.
(
SDUHSD Math B Honors Module #1 – HOMEWORK 2017-2018
)
; Evaluate for
3
(
14.
); Evaluate for
) 16. ( Evaluate for
(
15.
[
(
)]
17. ( Evaluate for
);
)
(
); Evaluate for
(
);
Directions: Simplify the expression without using Algebra tiles. Show all of your work. 18.
20. (
(
)
(
)
(
)
)
19.
(
21.
(
SDUHSD Math B Honors Module #1 – HOMEWORK 2017-2018
)
(
)
)
(
(
)
)
4
22. Evaluate (
)
(
) for
. Show all of your work.
Directions: Evaluate the given expression for
and
23.
24.
25.
26.
Show all of your work.
Spiral Review: 27. What is the probability of drawing a purple marble out of a bag with 8 green marbles, 4 purple marbles, 10 black marbles, and 2 red marbles?
28. 0.5% of what number is 15?
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1.1B Homework: Linear Expressions and Real-World Contexts* Name:
Period:
1. Keith bought 3 packs of Yu-Gi-Oh! cards. He already has 35 cards in his collection. a. Identify your unknown quantity. Write an expression that represents the total number of cards Keith has. Simplify your expression.
b. If each pack has 5 cards, how many total Yu-Gi-Oh! cards does Keith have?
2. Master Tickets charges $35 for each concert ticket, plus an additional $2 service fee for each ticket sold. a. Identify your unknown quantity. Write an expression that represents the total cost of the concert tickets. Simplify your expression.
b. If 4 concert tickets were purchased, what was the total cost?
3. Lena went shopping for decorations for her birthday party. She started with $20. She bought 4 bags of balloons that cost dollars each, 2 rolls of streamers that cost $2.25 each, and 1 pack of hats that cost $4.50. a. Identify your unknown quantity. Write an expression that represents the amount of money remaining. Simplify your expression.
b. If the price for one bag of balloons is $2.50, how much money did Lena have left?
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4. An official tennis court has a width that is 42 feet shorter than the length. a. Identify your unknown quantities. Write an expression that represents the perimeter of the tennis court. Simplify your expression.
b. If a tennis court has a length of 78 feet, what is the perimeter of the entire court?
5. At North Shoe Store, a pair of boots is $30 more than a pair of sandals. Aryanna purchased 2 pairs of boots and 3 pairs of sandals. a. Identify your unknown quantities. Write an expression for the total amount spent. Simplify your expression.
b. If a pair of sandals is $15, how much money did Aryanna spend?
6. At work, Nadia is paid time and a half (which means she is paid 1.5 times her normal hourly rate) for every hour she works over 40 hours. Last week, Nadia worked 50 hours. a. Identify your unknown quantities. Write an expression for the amount of money Nadia earned. Simplify your expression.
b. If Nadia earns $10.50 per hour, how much money did Nadia make last week?
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Directions: Write an expression that represents the word phrase. Then simplify the expression. 7. Twice the sum when a number y is added to three times a number x, increased by three times the sum when twice y is added to x.
8. The product of two and the cube of a number y, increased by six times the sum of three times the square of y and two times the cube of y.
Directions: Evaluate each expression for 9.
11.
and
and
. Show all of your work.
10.
(
)
12.
Spiral Review: 13. Simplify:
14. Math-r-us is having a 35% off sale on all calculators. If the calculator you want to buy is on sale for $18.00, what was the original price of the calculator?
15. The Noonan family drove hours to the Angels game. The trip home by another route took 20% less time. What was the family’s total travel time? Express your answers in minutes.
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1.1C Homework: Solving Linear Equations* Name:
Period:
) 1. For the equation ( model using Algebra tiles and explain your solving process. Solve algebraically and verify your solution. Model solving process:
Solve algebraically:
Verify your solution:
2. Complete the chart below: Equation
Tile Model
Written Description of Algebraic Procedure
SDUHSD Math B Honors Module #1 – HOMEWORK 2017-2018
Solve Algebraically
9
3. Justify and fill in the missing steps when solving the equation ( Step
)
Property/Justification
1.
Addition Property of Equality
2.
3.
4.
Multiplication Property of Equality
5.
Directions: A mistake was made when solving the equations below. Circle and explain the mistake made. Solve the equations correctly. (
4. Equation: (
)
Mistake made:
)
Equation solved correctly:
5. Equation: (
(
)
)
Mistake made:
Equation solved correctly:
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6. Equation:
(
)
Mistake made:
Equation solved correctly:
(
7. Equation:
)
Mistake made:
Equation solved correctly:
8. Equation:
(
)
(
)
(
)
Mistake made:
Equation solved correctly: (
9. Equation:
)
1 ( x 15) 11 3
Mistake made:
T Equation solved correctly: (
)
(
)
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Directions: Solve the following equations without using Algebra tiles. Verify your solutions and show all of your work. 10.
11.
Verify:
(
)
12.
Verify:
(
)
Verify:
Directions: Solve the following equations without using Algebra tiles. Show all of your work. 14.
13.
15.
(
)
(
16.
SDUHSD Math B Honors Module #1 – HOMEWORK 2017-2018
)
(
(
)
)
12
17.
18.
19.
20.
21.
23.
(
(
)
(
)
)
(
(
)
(
)
22.
)
25. Build an equation with a solution of
24.
(
)
(
)
that contains parentheses and requires adding like terms.
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1.1D Homework: Linear Equations and Real-World Contexts* Name:
Period:
Directions: Write a context that represents the given information and equation. Solve and write your solution in a complete sentence. Show all of your work. 1. Angles:
Context:
: :
Solution:
2. Ages
Context:
Felipe’s age now: f Felipe’s sister’s age now: Felipe’s mom’s age now: (
)
(
)
Solution:
3. A Trip to Disneyland
Context:
Miles driven on the first day: Miles driven on the second day: Miles driven on the third day:
m 2m (2m 50) 650
Solution:
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4. Triangles
Context:
x x (3x) 180
Solution:
5. The Cost of Clothes
Context:
Cost of a shirt: Cost of a pair of jeans:
3c (c 12) 124 Solution:
6. A Trip to the Fair
Context:
# of tickets for a pony ride: # of tickets to ride the Ferris wheel: # of tickets to bungee jump:
1 3b 4 b (2b 5) 33 2 Solution:
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Directions: Write an expression for each unknown quantity and an equation that represents the word problem. Solve your equation and write your solution in a complete sentence. Show all of your work. 7. The number of boys in the Sports Club is four fifths the number of girls. If there are 360 boys and girls altogether in the club, how many girls are there in the club?
8. Michaela’s age is ten years greater than half Jake’s age. If the sum of their ages is 55, how old is Michaela?
9. A certain molecule contains twice as many atoms of hydrogen as oxygen and one more atom of carbon than hydrogen. If there are 21 atoms altogether in the molecule, how many atoms of carbon are there?
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10. One number is 35 greater than a second number. If the lesser number is subtracted from twice the greater number, the difference is 87. Find the numbers.
11. The length of a certain rectangle is 3 cm less than twice its width. If each dimension were reduced by 5 cm, the resulting figure would have a perimeter of 16 cm. What are the dimensions of the original rectangle?
12. Joy has $11.25 in nickels, dimes and quarters. She has 3 times as many nickels as dimes and 5 more quarters than dimes. How many of each kind of coin does Joy have?
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1.1E Homework: Solving Linear Inequalities Name:
Period:
Directions: Solve each inequality. Show all of your work. State four values that satisfy the inequality and four values that do not. 1.
2.
Values that satisfy the inequality
Solution
(
)
Whole #:
Whole #:
Natural #:
Natural #:
Integer #:
Integer #:
Rational #:
Rational #:
Values that satisfy the inequality
Solution
Values that do not satisfy the inequality
Values that do not satisfy the inequality
Whole #:
Whole #:
Natural #:
Natural #:
Integer #:
Integer #:
Rational #:
Rational #:
Directions: Solve each inequality and graph its solution set on a number line. Show all of your work. 3.
4.
(
SDUHSD Math B Honors Module #1 – HOMEWORK 2017-2018
)
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5.
7.
9. If
(
)
(
(
)
)
(
)
, is the inequality
6.
8.
(
(
)
)
true or false? If false, give an example to justify your answer.
Directions: Write an expression for each unknown quantity and an inequality that represents the word problem. Solve your inequality and write your solution in a complete sentence. Show all of your work. 10. Jordyn needs $100 to buy a graphing calculator for her math class. Her neighbor will pay her $8 per hour to babysit and her father gave her $10 yesterday for mowing the lawn. What is the minimum amount of hours she needs to babysit in order to buy her calculator? Round your answer to the nearest whole hour.
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11. The length of a rectangle is 5 times its width. The perimeter of the rectangle is at most 104 feet. Find the greatest possible dimensions of this rectangle.
12. Find the least three consecutive integers whose sum is greater than -87.
13. The measure of is twice the measure of and the measure of is one more than the measure of . If the sum of the measures of all three angles is at least 56°, what is the least possible measure of ?
Spiral Review: 14. Solve each equation for the value of a.
(
)
when
and b.
SDUHSD Math B Honors Module #1 – HOMEWORK 2017-2018
Show all of your work. (
)
(
)
20
1.1F Homework: Solving Equations with Absolute Value Name:
Period:
Directions: Determine if the given statement is true or false. If false, provide an example to justify your reasoning. 1. The absolute value of any real number is equal to the absolute value of the opposite of the number.
2. The absolute value of any real number is greater than zero.
Directions: Simplify each expression. Show all of your work. 3.
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6.
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9.
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4. |
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7.
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10.
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(
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SDUHSD Math B Honors Module #1 – HOMEWORK 2017-2018
5.
|
8.
(
11.
|
)
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[ (
)]
|
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21
Directions: Solve the following equations. Show all of your work. 12.
| |
15. | |
18.
13.
|
|
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(| |
16.
| |
19.
(
)
)
| |
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14. | |
|
17.
| |
20.
(
|
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21. For which value(s) of
is the statement |
|
true? Explain your reasoning.
22. For which value(s) of
is the statement |
|
true? Explain your reasoning.
23. For which value(s) of
is the statement |
|
|
|
SDUHSD Math B Honors Module #1 – HOMEWORK 2017-2018
|)
true? Explain your reasoning.
22
Directions: Evaluate each expression when 24.
26. |
|
|
|
(
28. Solve
|
. Show all of your work.
|
)
(
|
)
|
for the value of
when
25.
|
[
27.
| |
| |
and
(
)]|
Show all of your work.
Spiral Review: 29. Simplify as a fraction:
̅
30. What is 98.5% of $140.32?
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1.1G Homework: Abstracting the Solving Process (Part 1)* Name:
Period:
Directions: Circle and explain the mistake made when solving for variables equal 0. Then solve for correctly.
in the equations below. Assume no
1.
Explain mistake made
Solve for
correctly
2.
Explain mistake made
Solve for
correctly
Explain mistake made
Solve for
correctly
(
3.
)
(
) [ ( (
)(
)]
(
)
)
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Directions: Solve the following equations for
if
and
4.
5.
6.
7.
8.
9.
10.
(
)
11.
represent real numbers not equal to 0.
(
)
(
)
Spiral Review: 12. The perimeter of a square is 11.6 inches. What is the area?
13. The degree measures of the angles of a triangle are consecutive even integers. What are the measures of the angles?
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Section 1.1: Review Name:
Period:
Directions: Simplify each expression and evaluate for the given value. Show all of your work. 1.
(
3.
[
)
(
(
)]
); evaluate for
evaluate for
5. Write three expressions that are equivalent to
6. For the equation ( your solution.
)
(
2.
4.
(
)
)
(
evaluate for
); evaluate for
.
model and explain your solving process. Solve algebraically and verify
Model solving process:
Solve algebraically:
Verify your solution:
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Directions: Solve the following equations or inequalities. Show all of your work. Classify your solution as a natural, whole, integer and/or rational number. (
8.
7.
(
9.
)
)
10.
Directions: Solve the following equations or inequalities. Show all of your work. 11.
(
)
(
13.
15.
| |
17.
(
12.
)
|
|)
| |
14.
16.
(
18.
(
SDUHSD Math B Honors Module #1 – HOMEWORK 2017-2018
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)
27
19.
(
)
(
)
20.
(
)
Directions: A mistake was made when solving the equations below. Circle and explain the mistake made. Solve the equations correctly. 21. Equation: (
)
Mistake made:
Equation solved correctly:
22. Equation:
(
)
Mistake made:
Equation solved correctly:
Directions: Write a context that represents the given information and equation. Solve and write your solution in a complete sentence. Show all of your work. 23. Triangles
(
Context:
)
Solution:
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24. Making Lemonade
Context:
Cups of water to make a batch of lemonade: Cups of sugar to make a batch of lemonade: Cups of lemon juice to make a batch of lemonade:
1 1 c c c 14 4 2
Solution:
Directions: Write an expression for each unknown quantity and an equation or inequality for the word problem. Solve your equation or inequality and write your solution in a complete sentence. Show all of your work. 25. The two longest sides of a pentagon are each 3 times as long as the shortest side. The other sides are each 8 inches longer than the shortest side. If the perimeter is 79 inches, what is the length of each side?
26. Jesse and her brothers Nick and Owen are saving money over the summer. Each week, Jesse saves twice as much as Owen. Owen saves $5 more than Nick. At the end of four weeks, the three of them have saved a total of $220. How much money does each person save each week.
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27. Laura has 98 coins in her wallet made up of dimes and quarters. The total value of the coins is $18.50. How many dimes and quarters does Laura have?
28. Oliver is 8 years older than his sister Thea. In four years, the sum of their ages will be 56. Find their current ages.
29. The dance committee hired a DJ for the fall dance. The DJ charges $125 per hour plus $55 for an assistant. The committee wants to keep the total cost under $600. What is the maximum amount of hours the DJ will play at the dance?
30. Allie went shopping at the mall and had $100 to buy a jacket and skirt. If the price of the jacket she bought was $20 more than 3 times the price of the skirt, what was the highest possible price of the skirt?
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1.2A Homework: Solving Multi-Step Linear Equations (with variables on both sides)* Name:
Period:
Directions: Every beam in the mobiles is balanced and the strings and beams weigh nothing. Find the weight of each shape. 1.
2.
36
Directions: Solve the following equations. Verify your solutions and show all of your work.
3. 3 y 12 3 y 12
Verify:
1 1 4. 3 x x 9 4 2
Verify:
Directions: Solve the following equations. Show all of your work. 5.
6. 2 (2 x 2) 2( x 3) x
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(
7.
9.
11.
13.
(
)
(
)
(
)
(
)
8.
)
(
12.
)
(
)
(
(
10.
(
)
(
)
)
)
(
(
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)
(
)
14.
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15. Write an equation that uses the distributive property on at least one side of the equation, variables on both sides of the equation, and a solution of .
Directions: A mistake was made when solving the equations below. Circle and explain the mistake made. Solve the equations correctly. 16. Equation: 4 x 8 2 x 20
Mistake made:
Equation solved correctly:
17. Equation:
(
)
(
)
Mistake made:
Equation solved correctly: (
)
(
)
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18. Equation: [
(
(
) [
)]
(
(
)
(
(
)
Mistake made:
)] ) Equation solved correctly:
Directions: Solve each inequality and graph the solution on a number line. Show all of your work. 19.
20.
21.
22.
23.
(
)
(
)
24.
(
(
SDUHSD Math B Honors Module #1 – HOMEWORK 2017-2018
)
)
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1.2B Homework: Solving Linear Equations with Different Solving Outcomes* Name:
Period:
Directions: Replace each ? in the equations below with a numerical or a variable expression so that the following conditions are satisfied. Justify your reasoning. 1.
(
)
2.
a. solution set is 0
a. solution set is 0
b. solution set is infinitely many solutions
b. solution set is infinitely many solutions
c. solution set is no solution
c. solution set is no solution
Directions: Fill in the blanks of the following equations to meet the given criteria. 3. An equation that yields no solution:
8x
4. An equation that yields infinitely many solutions:
x 10
8 x 24
x
Directions: Examine the structure of each equation. State if there are infinitely many solutions, no solution, or one solution. If there is one solution, solve the equation and state the solution. If there are infinitely many solutions or no solution, justify why using the structure of the equation. (
5.
7.
(
)
)
6.
8.
(
)
(
SDUHSD Math B Honors Module #1 – HOMEWORK 2017-2018
(
)
)
(
)
35
9.
(
)
| |
11.
13.
(
12.
)
(| |
10.
(
14.
)
15. Consider the equation (
(
)
)
(
(
)
)
(
)
)
a. Find one value for and one value for so that there is exactly one value of equation true. Explain your reasoning.
that makes the
b. Find one value for and one value for so that there are infinitely many values of equation true. Explain your reasoning.
that make the
Directions: Create your own equations with variables on both sides that meet the given criteria. 16.
An equation that yields one solution of
17.
An equation that yields no solution.
.
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18.
An equation that yields infinitely many solutions.
19.
An equation with two solutions.
20. Two students, Arthur and Oliver, each have some chocolates. They know that they have the same number of chocolates. Arthur has two tubs of chocolates, three bags of chocolates, and twenty-five loose chocolates. Oliver has two tubs of chocolates, five and a half bags of chocolates, and fifteen loose chocolates. Can you determine how many chocolates are in a tub? How many chocolates are in a bag?
21. Like Arthur and Oliver, Abby and Amy also say that they have the same number of chocolates. Abby has one full tub of chocolates and 21 loose chocolates. Amy has one full tub of chocolates and 17 loose chocolates. Each tub has the same number of chocolates. Can you determine how many chocolates are in a tub? Why or why not? If so, how many chocolates are in a tub?
Spiral Review: 22. Simplify:
(
)
23. At the end of the year sale at Byte Boys, a laptop was discounted 25% and sold for $315. What was the original price of the laptop?
24. Solve the equation (
)
(
)
(
)
for the value of when
SDUHSD Math B Honors Module #1 – HOMEWORK 2017-2018
and
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1.2C Homework: Solving Linear Equations to Model Real-World Contexts* Name:
Period:
Directions: Write a context that represents the given expressions and equation. Solve and write your solution in a complete sentence. Show all of your work. 1. Fixing Your Car
Context:
Number of hours it takes to fix your car: Cost of Mike’s Mechanics: 15h 75 Cost of Bubba’s Body Shop:
15h 75 25h
Solution:
a. Which shop would be a better deal if it took 4 hours to fix your car?
b. Which shop would be a better deal if it took 10 hours to fix your car?
2. World Languages
Context:
Number of years: Number of Students Enrolled in French: 160 9t Number of Students Enrolled in Spanish: 85 6t
Solution:
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3. Downloading Music
Context:
Number of songs downloaded: Monthly cost of downloading songs at bTunes: Monthly cost of downloading songs at iMusic:
Solution:
a. Which is a better deal if you download 10 songs per month? 20 songs per month?
b. Which is a better deal if you download 100 songs per month?
Directions: Define your variables and write an expression for each unknown quantity and an equation that represents the word problem. Solve your equation and write your solution in a complete sentence. Show all of your work. 4. Underground Floors charges $8 per square foot of wood flooring plus $150 for installation. Jimmy’s Hardwood Flooring charges $6 per square foot plus $200 for installation. At how many square feet of flooring would the two companies charge the same amount for flooring? If you were going to put flooring on your kitchen floor that had an area of 120 square feet, which company would you choose?
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5. Owen and Charlotte’s mom give them the same amount of money to spend at the fair. They both spend all of their money. Owen goes on 8 rides and spends $5 on pizza while Charlotte goes on 5 rides and spends $6.50 on pizza and ice cream. How much does each ride cost?
6. Ashton and Kamir are arguing about a number trick they learned. Ashton tells Andrew to think of a number, multiply it by five and subtract three from the result. Kamir tells Andrew to think of the same number, add five and multiply the result by three. Andrew says that whichever way he does the trick he gets the same answer. What is the number?
7. The length of a certain rectangle is 10m greater than twice its width. If the width were reduced by 20m and the length increased by 100m, the perimeter of the new rectangle would be twice the perimeter of the original rectangle. What are the dimensions of the original rectangle?
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8. Three times an odd integer is eleven less than four times the next greater integer. What is the odd integer?
9. Brooke collected some change in preparation for a garage sale. She collected two more nickels than twice the number of dimes and eight fewer quarters than twice the number of nickels. If the value of the quarters was $1.60 greater than four times the value of the nickels and dimes together, what was the total value of the change that Brooke collected?
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1.2D Homework: Examining Real-World Contexts without Solutions Name:
Period:
Directions: Write an expression for each unknown quantity and an equation or inequality to represent the word problem. Solve your equation or inequality and write your solution in a complete sentence. If the word problem has no solution, explain your reasoning. 1.
2.
and are supplementary angles. The measure of complement of ?
is twice the measure of
. What is the
A wallet contained 37 coins consisting of dimes and nickels. If the total value of the coins is $2.80, how many dimes are in the wallet?
3. Rory is four years older than Zemo. Five years from now, Rory will be twice Zemo’s age. How old is Rory now?
4.
The perimeter of a triangle is 165 cm. The first side is 65 cm less than twice the second side. The third side is 10 cm less than the second side. What are the lengths of each side?
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5.
Melissa’s average grade on her first six math tests was 75%. She got 100% on each of her next two tests. If the highest score on any possible test is 100%, what grades must Melissa get on the next two tests in order to have an average of 90% overall?
6. The sum of two consecutive integers is at least negative fifteen. What are the smallest values of consecutive integers that will make this true?
7.
Erin is four years less than three times Kelli’s age. Half of Erin’s age increased by Kelli’s age is two years more than twice Kelli’s age. Find the age of each girl.
Spiral Review: (
8. Simplify:
)
9. A certain kind of lumber costs $3 for 8 ft. At this rate, how much does a 14 ft. piece of lumber cost?
10. Evaluate each expression when a.
|
|
and
. Show all of your work. b.
(| |
SDUHSD Math B Honors Module #1 – HOMEWORK 2017-2018
| |)
43
1.2E Homework: Abstracting the Solving Process (Part 2)* Name: Directions: Solve the following equations for
Period: where
and
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
SDUHSD Math B Honors Module #1 – HOMEWORK 2017-2018
are real numbers not equal to 0.
44
11. The equation ( width, .
)
can be used to find the perimeter, , of a rectangle given length
a. Solve the equation for width,
and
.
b. If the perimeter of a rectangle is 18 meters and has a length of 4 meters, what is the width of the rectangle?
12. The equation
can be used to find the area, , of a triangle given a base
and height, .
a. Solve the equation for base, .
b. If the area of a triangle is 20 meters with a height of 5 meters, what is the length of the base of the triangle?
13. The equation bases .
(
) can be used to find the area
of a trapezoid given a height
and
a. Solve the equation for base .
b. If the area of a trapezoid is 377 length of base a?
with a height of 26 cm and length of base b of 14 cm, what is the
Spiral Review: 14. Emily answered 95% of the test questions correctly. If she answered 38 questions correctly, how many questions were on the test?
SDUHSD Math B Honors Module #1 – HOMEWORK 2017-2018
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Section 1.2: Review Name:
Period:
Directions: Solve the following equations. Verify your solutions and show all of your work. 1. 7( x 3) 3x 3( x 2)
Verify:
2.
(
)
(
)
3.
Verify:
(
)
Verify:
Directions: Solve the following equations or inequalities. Show all of your work. 4.
6.
5.
(
)
(
)
(
)
7.
SDUHSD Math B Honors Module #1 – HOMEWORK 2017-2018
(
)
(| |
)
46
8.
(
)
(
10.
12.
)
9.
(
11.
(
14. 4 s
)
1 3 8 s 2 4
)
(
)
13.
15.
SDUHSD Math B Honors Module #1 – HOMEWORK 2017-2018
(
)
47
16.
(
)
(
|
17.
)
|
(
)
18. Build an equation that contains variables on both sides and has a solution of
Directions: Evaluate each expression for 19.
,
and
. Show all of your work. | |
20.
|
|
21. Select all equations that have one solution. A. 2x + 2x + 2 = 4x + 2
C.
B. x + x – (x + x) = 2x – x + 2
D.
(
)
E. –3(–x – 2) = 3(x – 2)
22. Select all equations that have infinitely many solutions. A. 2x + x – 4 = –x – x – x + 2 – 6
C. x + 2x + 3 + 3 + 3 = 3(x + 3)
B. 4(x + 9) = 2(2x + 9) + (–18)
D. 7x – 9 = 2x – 5x – 9 E.
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23. Select all equations that have no solution. A. 6 + 2x = 2(x + 6)
C. 11x – (x + 5) = –2(–5x – 3)
B. 3(3x – 4) = –9x + 11
D. 3x – (x – x) = x + 4 E. 3x – x + 12 – 6x = 4(5 – 2x) – (–4x)
Directions: Solve for , where
and
are real numbers not equal to 0. Show all of your work.
24.
25.
26.
27.
Directions: Write an expression for each unknown quantity and an equation that represents each word problem. Solve your equation and write your solution in a complete sentence. If the word problem has no solution, explain why. 28. Cashel is 8 years older than his sister Delaney. Next year, he will be three times as old as Delaney. How old is Cashel now?
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29. The length and width of a rectangle are consecutive odd integers. The perimeter of the rectangle is 49 cm. What are the dimensions of the rectangle?
30. Yoshi’s age is two years more than twice Mario’s age. The sum of their ages is the same as the age of Princess Peach. If Princess Peach’s age is 10 years less than five times Mario’s age, what are the ages of each person?
31. Susan has twice as many dimes as nickels and 10 more quarters than half the amount of nickels. If the total value is $4.75, how many of each type of coin does Susan have?
SDUHSD Math B Honors Module #1 – HOMEWORK 2017-2018
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