Solve Linear and Absolute Value Inequalities

What is the correct first step?

• divide by 10

• multiply by 10

• make it two inequalities with an "or"

• make it two inequalities with and "and

| -8x | < 8

What is the correct first step?

• separate into two inequalities with an "and"

• separate into two inequalities with an "or"

• divide both sides by -8

• add 8 to both sides

The radius of the gears produced at a factory must be 6 inches in length with a tolerance of 0.1 inches. The gears with radius beyond the tolerated lengths will be thrown away. Which of the following inequalities can be used to assess which gears are eligible? (x is the length of the radius)

• |x – 6| ≤ 0.1
• |x – 6| ≥ 0.1
• |x – 0.1| ≤ 6
• |x – 0.1| ≥ 6

The average temperature in Las Vegas in July is 110 degrees.  If the temperature can vary up to 10 degrees, which equation represents this situation?

• | x - 10 | < 110
• | 110 - x | < 10
• | x - 110 | < 10
• | 10 - x | < 110

Write an inequality for Graph 3.

• x ≤ -2 AND x > 5
• x ≤ -2 OR x > 5
• x ≥ -2 OR x < 5
• -2 ≤ x < 5

| x - 6 | < 4
Is this an "and"  or an "or" problem?

• and
• or

Solve for c when | 3c - 5 | is less than or equal to -2

• No Solution

• All Real Numbers

• 1 < c < ⁷/₃

• c < 1 or c > ⁷/₃

Solve for w, when | 12 + w | is greater than or equal to -5

• No Solution

• All Real Numbers

• w ≤ -17 or w ≥ -7

• -17 ≤ w ≤ -7

John is looking for a job after graduation. The salary which he is satisfied with must be $3000 with a tolerance of $500. Choose the salary John would accept.

• $3,478
• $3,792
• $2,489
• $2,256

In order to enter the kiddie rides at the amusement park, a child must be between the ages of 4 and 10. Let a represent the age of a child who may go on the kiddie rides.

• |a-14| less than or = 6

• |a+14| greater than or = 6

• |a-7| less than or = 3

• |a+7| greater than or = 3