Linear inequalities (one variable)

On the interstate for someone to get a ticket for speed, they must be less than 45 mph or greater than 75 mph. What absolute value inequality describes the speeds of those receiving a ticket?

• |x-120| less than or = 30

• |x-60| less than or = 15

• |x+120| greater than or = 30

• |x+60| greater than or = 15

What has to be done first in order to solve this inequality?

• subtract 3 from both sides

• distribute the 3

• divide both sides by 3

• nothing

Solve the inequality. 
|3 + r|/7 < 5

• r < 32
• -38 < r < 32
• r < -38
• No solution

|b-8|+10>22

• -4<b<20

• b<-4 or b>20

• 20<b<-4

• b=-4 or b=20

What is the correct first step?

 |x + 3| > 8

• Set up two cases with "and"

• Set up two cases with "or"

• Subtract 3 from both sides

During a recent visit to the veterinarian’s office, Mrs. Allen was informed that a healthy weight for her cat is approximately 10 pounds, plus or minus one pound. Write an absolute value inequality that represents unhealthy weights w for her cat.

Solve:
3 | 2x + 7| - 7 < -4

• all real numbers
• no solution

Solve the absolute value inequality: |3x + 2| ≥ 10

• x ≤ -6 or x ≥ 4

• x ≤ -2 or x ≥ 6

• x ≤ -8 or x ≥ 12

• x ≤ -4 or x ≥ 2

Solve the following absolute value inequality:

5|x + 4| − 8 > 2

• x > -2 or x < -6

• x > 2 or x < 6

• -2 < x < -6

• -6 < x < -2