Inequalities & Absolute Value

Evaluate.
| 15 - 5 | =

• 20

• 10

• -20

• -10

Solve: -3 ≤ 2x - 1 ≤ 5

• -1 ≤ x ≤ 3

• -2 ≤ x ≤ 6

• -3 ≤ x ≤ 3

• 1 ≤ x ≤ 3

3x + 2 < -7 or -4x + 5 < 1

• All real numbers

• x < -3 and x > 1

• x < -3 or x < 1

• x < -3 or x > 1

Which of the following would result in NO SOLUTION?

• x < 1 or x > 5

• x > 1 or x < 5

• x < 1 and x > 5

• x > 1 and x < 5

-4x + 14 ≤ 54

• x ≥ - 10

• x ≤ -10

• x ≥ 10

• x ≤ 10

Solve:
3(x - 2) < 2(x + 9)

• x<24

• x>12

• x<12

• x>24

You flip an inequality symbol when you...

• subtract

• multiply and divide only

• multiple by a negative number

• multiple or divide by a negative number

Your family needs 2 gallons of water this week, but you don’t want to buy any more than 8 gallons. Write an inequality representing the possible gallons of water you could buy this week.

• 2 ≤ x ≤ 8

• 2< x < 8

• 8 ≥ x ≥ 2

• 2> x > 8

A taxi cab costs $1.75 and $0.75 for each additional mile. You have $20 to spend on you ride. Which inequality could be solved to find how many miles you can travel, if m is the number of additional miles?

• 1.75n + 0.75 ≥ 20

• 1.75n + 0.75 ≤ 20

• 0.75n + 1.75 ≥ 20

• 0.75n + 1.75 ≤ 20

Solve 24 > -3r > -9 

• -8 < r < 3

• -8 > r > 3

• r > - 8 and r > 3 

• r > -8 or r < 3