Algebra I SOL Review
Equations & Inequalities
Name _________________________
1. Look at the system of equations
𝑦 = −𝑥 + 2
{
}
7𝑥 + 4𝑦 = −1
What is the value of 𝑥 for the solution to this system of equations?
2. Pierre solves an inequality as shown.
Step 1: −8 ≥ 𝑛 + 3
Step 2: −8 + (−3) ≥ 𝑛 + 3 + (−3)
Step 3: −11 ≥ 𝑛 + 0
Step 4: −11 ≥ 𝑛
What property justifies the work between Step 3 and Step 4?
a.
Inverse property of addition
b. Identity property of addition
c.
Addition property of inequality
d. Commutative property of addition
3.
Which property of real numbers justifies the work shown?
13𝑥 − 1 = (12𝑥 + 15) + 7𝑥
13𝑥 − 1 = 7𝑥 + (12𝑥 + 15)
a.
Commutative property of addition
b. Associative property of addition
c.
Identity property of addition
d. Distributive property
Algebra I SOL Review
Equations & Inequalities
Name _________________________
1
8
4.
What is the slope of the line represented by 𝑥 + 3𝑦 = 3?
5.
Solve for 𝑥:
6.
Graph 𝑦 ≤ 𝑥 − 2
7.
Which inequality represents all the solutions of 9(4𝑥 − 8) < 4(6𝑥 + 9)?
− 2𝑥 + 6 < 𝑥 − 6
2
7
a.
𝑥 < −3
c. 𝑥 < 9
b. 𝑥 > −3
d. 𝑥 > 9
Algebra I SOL Review
Equations & Inequalities
8.
Name _________________________
A total of 243 adults and children are at a movie theatre. There are 109 more adults than children
in the theatre. If a represents the number of adults and b represents the number of children,
which system of equations could be used to find the number of adults and the number of
children in the theatre?
9.
𝑎 + 𝑏 = 243
a. {
}
𝑎 = 109𝑏
𝑎 + 𝑏 = 243
b. {
}
𝑏 = 109𝑎
𝑎 + 𝑏 = 243
c. {
}
𝑎 = 𝑏 + 109
𝑎 + 𝑏 = 243
d. {
}
𝑏 = 𝑎 + 109
Find the solutions to the following inequality:
1
𝑦 > 2𝑥 + 1
{
}
𝑦 + 3𝑥 ≤ 6
10. The formula shown can be used to find A, the amount of money Raul has in his saving account.
𝐴 = 𝑃 + 𝑃𝑟𝑡
Raul wants to find r, the rate of interest his money earns. Which equation is correctly solved for r?
a.
𝑟 = 𝐴𝑃𝑡
c.
𝑟 = 2𝑃𝑡
𝐴
b. 𝑟 = 𝐴 − 2𝑃𝑡
d. 𝑟 =
11. What are the real roots of 𝑥 2 − 7𝑥 + 10 = 0?
𝐴−𝑃
𝑃𝑡
Algebra I SOL Review
Equations & Inequalities
Name _________________________
12. A data set with an even number of data points is ordered from least to greatest. The middle two
data points are represented by 𝑥1 and 𝑥2 . This formula can be used to find the median of the data
set.
𝑚=
𝑥1 + 𝑥2
2
Which shows this formula solved for 𝑥1 ?
a.
𝑥1 = 𝑚 −
c.
𝑥1
𝑥2
2
= 2𝑚−2𝑥2
b.
𝑥1 = 2𝑚 − 𝑥2
d. 𝑥1 = 𝑚 − 2 − 𝑥2
13. Which equation represents the horizontal line passing through (7,5) ?
a.
𝑥=5
b. 𝑦 = 5
c.
𝑥=7
d. 𝑦 = 7
14.
What are the solutions to 𝑥 2 − 2𝑥 − 8 = 0?
Algebra I SOL Review
Equations & Inequalities
Name _________________________
15. What value of p will make this equation true?
6𝑝 + 4
4𝑝 − 8
=
6
3
a.
−10
b. -6
c.
2
d. 10
16. What is the slope of the line represented by this equation?
3𝑥 + 5𝑦 = −7
17. The length, l, of a rectangle is 3 times its width. The perimeter of the rectangle is greater than 48
centimeters. Which inequality expresses all the possible lengths, in centimeters, of the rectangle?
a.
𝑙>6
b. 𝑙 > 12
c.
𝑙 > 18
d. 𝑙 > 36
18. Graph the equation 4𝑥 + 5𝑦 = −20
Algebra I SOL Review
Equations & Inequalities
Name _________________________
19. A formula to find the angle measure of an isosceles triangle is shown.
180 = 2𝑥 + 𝑦
Which equation can be used to find 𝑥?
180−𝑦
a.
𝑥=
c.
𝑥 = 90 − 𝑦
2
b.
𝑥 = 180+𝑦
2
d.
𝑥 = 90 + 𝑦
20. Which equation represents the line that passes through the points (-4, 4) and (8, -2) ?
a.
𝑦 = −2𝑥 + 14
b. 𝑦 =
−1
2
b. 𝑦 = −2𝑥 − 4
d. 𝑦 =
𝑥+2
−1
2
𝑥−2
21. For which system of inequalities is (-3, 1) a solution?
a.
𝑥 + 𝑦 < −2
{
2𝑥 − 3𝑦 < −9
𝑥 + 𝑦 < −2
b. {
2𝑥 − 3𝑦 ≤ −9
c.
x + y ≤ −2
{
2x − 3y < −9
x + y ≤ −2
d. {
2x − 3y ≤ −9
22. What is the solution to this system of equations?
2𝑥 + 4𝑦 = 22
{
7𝑥 + 𝑦 = 12
Algebra I SOL Review
Equations & Inequalities
23.
24. What are the solutions to −𝑥 2 − 2𝑥 + 8 ?
25. What value of 𝑥 makes this equation true?
3𝑥 − 20 = −2𝑥
Name _________________________
Algebra I SOL Review
Equations & Inequalities
Name _________________________
26. Christopher incorrectly solved an inequality as shown.
Step 1: −4(𝑥 − 7) + 1 ≤ −3
Step 2: −4(𝑥 − 7) ≤ −4
Step 3: −4𝑥 + 28 ≤ −4
Step 4: −4𝑥 ≤ −32
Step 5: 𝑥 ≤ 8
Between which two consecutive steps did Christopher make a mistake?
27. Solve for 𝑛:
3𝑛−7
6
=
2𝑛+5
3
28. Based on the transitive property, complete this statement:
If 2(𝑦 − 3) ≥ 3𝑥 − 4 and 3𝑥 − 4 ≥ 6 − 𝑦, then 2(𝑦 − 3) ≥ _____________
Algebra I SOL Review
Equations & Inequalities
Name _________________________
29. Renee is going bowling.

The cost per game is $2.50

Renee will need to rent a pair of bowling shoes for $1.50

She can spend up to $16.00 to bowl and rent a pair of shoes.
What is the maximum number of games that Renee can bowl?