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You solved one-step and multi-step inequalities.
• Solve compound inequalities.
• Solve absolute value inequalities.
• compound inequality
• intersection
• union
Solve an “And” Compound Inequality
Solve 10  3y – 2 < 19. Graph the solution set on a
number line.
Method 1 Solve separately.
Write the compound inequality using the
word and. Then solve each inequality.
10  3y – 2
and
3y – 2 < 19
12  3y
3y < 21
4 y
y<7
4y<7
Solve an “And” Compound Inequality
Method 2 Solve both together.
Solve both parts at the same time by
adding 2 to each part. Then divide each
part by 3.
10  3y – 2 < 19
12 
3y
< 21
4
y
<7
Solve an “And” Compound Inequality
Graph the solution set for each inequality and find their
intersection.
y4
y<7
4y<7
Answer:
Solve an “And” Compound Inequality
Graph the solution set for each inequality and find their
intersection.
y4
y<7
4y<7
Answer: The solution set is y | 4  y < 7.
What is the solution to 11  2x + 5 < 17?
A.
B.
C.
D.
What is the solution to 11  2x + 5 < 17?
A.
B.
C.
D.
Solve an “Or” Compound Inequality
Solve x + 3 < 2 or –x  –4. Graph the solution set on
a number line.
Solve each inequality separately.
x+3 <2
x < –1
or
–x  –4
x4
x < –1
x4
x < –1 or x  4
Answer:
Solve an “Or” Compound Inequality
Solve x + 3 < 2 or –x  –4. Graph the solution set on
a number line.
Solve each inequality separately.
x+3 <2
x < –1
or
–x  –4
x4
x < –1
x4
x < –1 or x  4
Answer: The solution set is x | x < –1 or x  4.
What is the solution to x + 5 < 1 or –2x  –6?
Graph the solution set on a number line.
A.
B.
C.
D.
What is the solution to x + 5 < 1 or –2x  –6?
Graph the solution set on a number line.
A.
B.
C.
D.
Solve Absolute Value Inequalities
A. Solve 2 > |d|. Graph the solution set on a
number line.
2 > |d| means that the distance between d and 0 on a
number line is less than 2 units. To make 2 > |d| true,
you must substitute numbers for d that are fewer than
2 units from 0.
Notice that the graph of
2 > |d| is the same as the
graph of d > –2 and d < 2.
All of the numbers between –2 and 2 are less than
2 units from 0.
Answer:
Solve Absolute Value Inequalities
A. Solve 2 > |d|. Graph the solution set on a
number line.
2 > |d| means that the distance between d and 0 on a
number line is less than 2 units. To make 2 > |d| true,
you must substitute numbers for d that are fewer than
2 units from 0.
Notice that the graph of
2 > |d| is the same as the
graph of d > –2 and d < 2.
All of the numbers between –2 and 2 are less than
2 units from 0.
Answer: The solution set is d | –2 < d < 2.
A. What is the solution to |x| > 5?
A.
B.
C.
D.
A. What is the solution to |x| > 5?
A.
B.
C.
D.
B. What is the solution to |x| < 5?
A. {x | x > 5 or x < –5}
B. {x | –5 < x < 5}
C. {x | x < 5}
D. {x | x > –5}
B. What is the solution to |x| < 5?
A. {x | x > 5 or x < –5}
B. {x | –5 < x < 5}
C. {x | x < 5}
D. {x | x > –5}
Solve a Multi-Step Absolute Value Inequality
Solve |2x – 2|  4. Graph the solution set on a
number line.
|2x – 2|  4 is equivalent to 2x – 2  4 or 2x – 2  –4.
Solve each inequality.
2x – 2  4
or
2x – 2  –4
2x  6
2x  –2
x3
x  –1
Answer:
Solve a Multi-Step Absolute Value Inequality
Solve |2x – 2|  4. Graph the solution set on a
number line.
|2x – 2|  4 is equivalent to 2x – 2  4 or 2x – 2  –4.
Solve each inequality.
2x – 2  4
or
2x – 2  –4
2x  6
2x  –2
x3
x  –1
Answer: The solution set is x | x  –1 or x  3.
What is the solution to |3x – 3| > 9? Graph the
solution set on a number line.
A.
B.
C.
D.
What is the solution to |3x – 3| > 9? Graph the
solution set on a number line.
A.
B.
C.
D.
Write and Solve an Absolute Value
Inequality
A. JOB HUNTING To prepare for a job interview,
Hinda researches the position’s requirements and
pay. She discovers that the average starting salary
for the position is $38,500, but her actual starting
salary could differ from the average by as much as
$2450. Write an absolute value inequality to
describe this situation.
Let x = the actual starting salary.
The starting salary can differ
by as much as $2450.
from the average
|38,500 – x|
Answer:

2450
Write and Solve an Absolute Value
Inequality
A. JOB HUNTING To prepare for a job interview,
Hinda researches the position’s requirements and
pay. She discovers that the average starting salary
for the position is $38,500, but her actual starting
salary could differ from the average by as much as
$2450. Write an absolute value inequality to
describe this situation.
Let x = the actual starting salary.
The starting salary can differ
by as much as $2450.
from the average
|38,500 – x|
Answer: |38,500 – x|  2450

2450
Write and Solve an Absolute Value
Inequality
B. JOB HUNTING To prepare for a job interview,
Hinda researches the position’s requirements and
pay. She discovers that the average starting salary
for the position is $38,500, but her actual starting
salary could differ from the average by as much as
$2450. Solve the inequality to find the range of
Hinda’s starting salary. | 38,500 – x |  2450
Rewrite the absolute value inequality as a compound
inequality. Then solve for x.
–2450  38,500 – x  2450
–2450 – 38,500 
–x
 2450 – 38,500
–40,950 
–x
 –36,050
40,950 
x
 36,050
Write and Solve an Absolute Value
Inequality
Answer:
Write and Solve an Absolute Value
Inequality
Answer: The solution set is x | 36,050  x  40,950.
Hinda’s starting salary will fall within $36,050
and $40,950.