Rev. 9/12
Name: _________________________________________
Hour: ___________
Algebra 1 Review
Linear Inequalities
Write the correct response on the line.
_____ 1. Which graph represents the solution. 𝑥 − 10 > 7
(1 pt)
a.
12 13 14 15 16 17 18 19 20 21 23
b.
12 13 14 15 16 17 18 19 20 21 23
c.
2
3
4
5
6 7
8 9 10 11 12
2
3
4
5
6 7
8 9 10 11 12
d.
_____ 2. Describe the solution of the compound inequality
−2𝑥 − 10 ≥ 2 or 5𝑥 + 1 > 11
a.
b.
c.
d.
All real numbers less than –4 or greater than 0.
All real numbers greater than -6 or less than 2.
All real numbers less than -6 or greater than 2.
All real numbers less than –4 and greater than 2.
_____ 3. Choose the inequality whose solution is shown in the graph.
a.
b.
c.
d.
(1 pt)
y  2 x  4
y  2 x  4
y  2 x  4
y  2x  4
(1 pt)
Rev. 9/12
_____ 4. Write an equation in slope-intercept form of the line that passes through
the points;
(1, 4) and (0, 5)
(1 pt)
a. 𝑥 + 𝑦 = 5
b. 𝑦 = 𝑥 − 5
c. 𝑦 = −𝑥 + 4
d. 𝑦 = −𝑥 + 5
5. Write the equation of the line shown in the graph.
(2 pt)
Equation: _____________________
6. Solve.
−𝟔 ≤ 𝟖𝒙 + 𝟏𝟎 ≤ 𝟏𝟒
(2 pt)
Solution: ___________________
7. Solve and graph
|5 – 2x| < 1.
(3 pts)
Solution: ________________________
8. Solve.
2 − 6𝑥 ≤ 10 ?
(3 pt)
Solution: ________________________
Rev. 9/12
9. Which numbers are solutions to the absolute-value equation
|𝑥 − 4| + 7 ≥ 8
(3 pt)
Solution: _____________________
10. In the last quarter of a high school football game, your team is behind by 35 points.
A field goal is 3 points and a touchdown (with the point-after-touchdown) is 7 points.
Let x represent the number of field goals scored. Let y represent the number of
touchdowns scored.
Write and graph an inequality that models the different numbers of field goals
and touchdowns your team would have to score in order to either win the game, or tie and send
it into overtime. (Assume the other team scores no more points.)
(6 pts)
Inequality: __________________________
11. Use the information in item 10 to respond to the following question.

(3 pts)
Does every point on the graph represent a solution of the real-life problem?
___________________________________________________________________

Explain your response.
___________________________________________________________________

Give three real-life examples to support your answer.
____________________________________________________________________
Rev. 9/12
12. Erin and Beth are on the Student Council Committee in charge of raising money for
purchasing a sound system for the school. The sound system costs $1,200. They
currently have $300 in the treasury. To raise the money the committee thinks they
can sell spirit items and baked goods every morning before school and at lunch,
which could net $75 per week. They have exactly 12 weeks to raise the money.
Do they have enough time to raise the money?
Erin solves the problem
300 + 75x >
300 – 300 + 75x >
75x >
75
x >
1200
1200 – 300
900
75
12 weeks
Erin reports that more than
12 weeks are needed.
1.
2.
3.
4.
(4 pts)
Beth solves the problem
1200 – 75x ≤ 300
1200 -1200 -75x ≤ 300 - 1200
-75x ≤ -900
-75
-75
x ≤ 12 weeks
Beth reports that at most 12 weeks
are needed. It can be done!
Are either of the inequalities set up correctly to solve this problem?
If so, which?
Are they solved correctly?
Who gives the correct recommendation?
1. ____________
2. ____________
3. ____________
4. ____________