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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 and3y – 2 < 19
12 3y3y < 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.
Answer:
x < –1
x 4
x < –1 or x 4
Solve each inequality separately.
–x –4orx + 3 < 2
x < –1 x 4
Solve an “Or” Compound Inequality
Solve x + 3 < 2 or –x –4. Graph the solution set on a number line.
Answer: The solution set is x | x < –1 or x 4.
x < –1
x 4
x < –1 or x 4
Solve each inequality separately.
–x –4orx + 3 < 2
x < –1 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.
Answer:
All of the numbers between –2 and 2 are less than 2 units from 0.
Notice that the graph of 2 > |d| is the same as the graph of d > –2 and d < 2.
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.
Answer: The solution set is d | –2 < d < 2.
All of the numbers between –2 and 2 are less than 2 units from 0.
Notice that the graph of 2 > |d| is the same as the graph of d > –2 and 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.
Answer:
The starting salary can differ from the average by as much as $2450.
|38,500 – x| 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.
Answer: |38,500 – x| 2450
The starting salary can differ from the average by as much as $2450.
|38,500 – x| 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 –36,05040,950 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.