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Math 8 Unit 3 Study Guide— Linear Equations in 1 Variable (Equal or Not)
Standard M8A1: Students will use algebra to represent, analyze, and solve problems. You
should be able to:
M8A1-a. Represent a given situation using algebraic expressions or equations in one variable.
1. Gene brought $60 to an amusement park. He spent d dollars while he was there. When
he left the amusement park, he had $15. Which mathematical sentence models this
situation?
a. 60 – d = 15
b. 15d = 60
c. d – 60 = 15
d. d - 15 = 60
2. Jorge belongs to a science fiction book club that sends 3 books each month. If he
started with a collection of 38 books, which equation below can he use to find out how
many months it will take to fill his bookshelf, which will hold 64 books?
a. 64 = 38m + 3
b. 64 = 3m + 38
c. 3(38) + m = 64 d. 3m + 38 = 64
3. Which mathematical sentence correctly models the word sentence: twelve more than
twice a number is 26?
a.. 2x + 12 = 26
b. x + 2 + 12 = 26 c. 2x  12 = 26
d. 12x + 2= 26
M8A1-b. Simplify and evaluate algebraic expressions.
5
7
4. What is the value of the 3m + 5n, when m =  and n =
?
10
6
a. -6
b. -1
c. 1
d. 6
5. Which shows the expression correctly simplified?
6g2 – g – 9 – (-4g2 + g – 4)
a. 2g2 – 2g – 13
b. 10g2 – 2g – 5
c. 2g2 – 13
HINT
Locate the “Understood 1” and
use the Distributive Property to
remove the parenthesis
d. 10g2 – 5
6. A computer technician charges $40 for a house call and $38 per hour. The expression
used to find the cost is: 40 + 38t In this expression, t is the time in hours. What is the
total cost, in dollars, of a repair if the house call lasts 3 hours?
a. $81
b. $154
c. $158
d. $234
M8A1-c. Solve algebraic equations or inequalities in one variable, including those involving
absolute value.
Multi-Step Equations:
Steps and Procedures:
1.
2.
3.
4.
5.
If necessary, use the Distributive Property to remove any parentheses
Identify & combine like terms
Add or subtract
Multiply or divide to solve for the variable and find the solution
Check your solution by substituting it back into the original problem
7. Solve the following equation for x.
a. x = 5
b. x = 4
4x  8
6
2
c. x = 3
d. x = 2
Absolute Value Equations:
Steps and Procedures:
1.
2.
3.
4.
If necessary, isolate the absolute value portion of the equation.
Clear the absolute-value bars by splitting the equation into its two possible two solutions, one solution for each sign
(+ & -).
Solve for the variable in both equations.
Check your solutions by substituting them back into the original problem.
8. How many solutions are there to the equation |5x – 20| = 100?
a. 0
b. 1
c. 2
d. infinite
9. 8|y|= 56
a. -448 and 448
b. -48 and 48
c. -7 and 7
d. -6 and 6
Equations with Variables on Both Sides:
Steps and Procedures
1.
2.
3.
4.
5.
If necessary, use the Distributive Property to remove any parentheses
Combine like terms that on the same side of the equal sign (if any exist)
Combine like terms so that all variable terms are on one side of the equation and rational numbers are on the other side
of the equation
Solve for the variable
Check your solution by substituting it back into the original problem
10. 2(x -1) = 4x + 12
a. 7
b. -7
c. 5
d. -5
M8A1-d. Solve equations involving several variables for one variable in terms of the others.
Steps and Procedures
1. Locate the variable you are asked to solve for in the equations
2. Identify the operations on the variable and the order in which they are applied
3. Use inverse operations to undo operations and isolate the variable
11. 3x + y = -6 for y
a. y = -3x
b. y = -3x + 6
c. y = -3x – 6
d. y = 3x – 6
12.
a
- c = d for a
b
a. a = bd + bc
b. a = bd – bc
c. a =
d +c
b
d. a =
d -c
b
M8A1-e. Interpret solutions in problem contexts
13. Sarah wants to buy a video game that costs $54, including tax. She already has $36
saved. She can save $9 per week. How many weeks will she have to save to have enough
money to buy the video game?
a. 2
b. 3
c. 4
d. 6
14. A cab ride costs $5 for the first mile and $4 for each additional mile. Carlo’s cab ride
cost $13. How many miles was the ride?
a. 2
b. 3
c. 4
d. 5
Standard M8A2: Students will understand and graph inequalities in one variable.
M8A2-a. Represent a given situation using an inequality in one variable.
15. Trey needs at least $60 to buy a new pair of sneakers. Sam already has $12, and his
parents have agreed to pay him $6 an hour to do gardening work.
Which inequality can be written to find h, the number of hours that Trey must do
gardening work in order to have enough money to buy a new pair of sneakers?
a. 6h – 12  60
b. 6h + 12  60
c. 6h – 12  60
d. 6h + 12  60
M8A2-b. Use the properties of inequality to solve inequalities.
16. Solve: |x + 3| > 7
a. x  4; x  -10 b. x  -4; x  10
x
 20  30
5
a. x > 2
b. x < 50
c. x  4; x  -10
d. x  -4; x  10
c. x > 50
d. x < 550
c. n  -8
d. n  -8
17. Solve:
18. -9n + 8  80
a. n  8
b. n  8
M8A2-c. Graph the solution of an inequality on a number line.

19. Which graph represents the solution to the inequality -1.3x > 9.1?
a. 
b. 
c. 
d. 
20. Which inequality has the solution shown in this graph?
---l---l---l---l---l---l---l---l---l---l---l---l---l---l---l---l---l---l---l---9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
a. -3x + 1 < 10
b. 2x -1 < -7
c. 3x – 2 < 7
d. 3x – 5 < 7
M8A2-d. Interpret solutions in problem contexts.
21. As part of his fitness plan, Jack wants to consume no more than 1,900 calories per day.
So far today, he has consumed 360 calories. He intends to eat 5 more small meals today.
What is the average number of calories he can consume per meal?
Which inequality matches the problem?
a. 5c + 360 > 1,900 b. 5c – 360  1,900
c. 5(c + 360)  1,900 d. 5c + 360  1,900
Which sentence is the solution?
a. c > 308
b. c < 308
c. c > 380
d. c < 380