Algebra 1
Chapter 6 Study Guide
Name ____________________________
Hour __________
Show ALL your work!
1. Solve the inequality. Then graph its solution.
a.
y+5>2
–10
c.
–5
b.
0
5
–10
–5
–10
10
-1.4x < -11.2
d.
0
5
10
x
4 < -2
–5
0
5
10
0
5
10
1
t < -2.4
4
–10
–5
2. Connie takes at least 47 seconds, s, to recite a poem. Write and graph an inequality to describe
this situation.
3. Write the inequality illustrated by the graph below.
4. Ken earns $5.65 per hour working after school. He needs at least $245 for a stereo system. Write
and solve an inequality that describes how many hours he must work to reach his goal.
5. You want to plant part of your field with wheat. The field is 150 feet wide and you have enough
seeds to plant at most 18,000 square feet. How long can the wheat field be?
6. Solve the inequality
a. 7x + 8 < 35(0.2x + 1)
–10
–5
0
b. 20(x + 3) > 10(2x – 3)
5
10
c. -7( 4x – 3) < -7
–10
–5
–10
–5
0
5
10
5
10
d. 8x – 9 > 9x + 2
0
5
10
–10
–5
0
7. Holly sells ice cream cones at the county fair. She has to rent the equipment for $48 and spend
$0.53 on ingredients for each cone. Write an inequality to represent the possible numbers of ice
cream cones that she must sell at $1.40 each in order to make a profit.
8. Your veterinarian tells you that a healthy weight for your dog is between 70 and 80 pounds. Write
an inequality to represent your dog's healthy weight w in pounds.
9. Graph the solution to the inequality "x is greater than 3 or less than or equal to 0."
10. Solve and graph your solution.
a. -6 < 3x – 15 < 12
b. 4 < 2 (1 – 3x) < 10
11. Solve the equation or inequality, then graph your solution.
a. 3x < 8 or 4x > 4
b. x + 5 > x + 7 or
c. 2x > 8 or -2x + 1 > -13
d. | x – 4| = 9
e. |x| < 5
f. | x | > 4
x + 3 < 3x - 4
12. Solve and graph
a. | 4x – 2 | < 3
b. | x + 7 | > 9
c. | 3x + 2 | < 1
d. |2x -1 | - 2 > 12
13. Graph the following.
a. –y > x – 1
10
b. x < -7
y
10 x
–10
10
c. y < 4x + 4
–10
y
10
d. 3x – 2y > -14
10 x
–10
10 x
–10
–10
10
y
–10
14. Is the ordered pair (–3, 7) a solution of the inequality 5x – 4y < -20?
y
10 x
–10
–10
15. Is the ordered pair (2, -4) a solution for the inequality 2x – 4y > 20?
16. You have $4500 to buy stock and have decided on American Enterprises (AE) and Allied Junk
Yards (AJY). AE sells for $27.50 per share and AJY sells for $45.25 per share. Write an
inequality that describes the possible numbers of AE shares and AJY shares you can buy.
17.
Give the equation of the inequality below:
a.
b.
c.
d.