Solving Inequalities with Absolute Value

Solve the following inequality:

−5|x − 4| > −20

• x < 8 and x > 0

• x > 8 or x < 0

• all real numbers

• no solution

Solve:
 |x + 3| > 8

• x > 5 or x < -11

• -11 < x < 5

• x > 11 or x < -5

• -5 < x < 11

What is the correct first step?

• divide both sides by 10

• multiply both sides by 10

• make it two inequalities with an "or"

• make it two inequalities with and "and" or a between statement

What is ALWAYS the first GOAL in solving an absolute value inequality?

• set up the positive case

• set up the negative case

• isolate the absolute value expression

• multiply or divide by the coefficient of the variable

∣ 2x + 9 ∣ = 15

• x = 3 

• x = 3
  x = -6

• x = 3
  x = -12

• x = 6
  x = -12

|v + 8| − 5 = 2 

• {-1,-15}

• {-1,-5}

• {-15,15}

• No Solution

| 2x + 12 | < 8

Which is the correct first step?

• 2x + 12 < 8 and 2x+12 > -8

• 2x + 12 < 8 or 2x+12 > -8

• 2x + 12 < 8 and 2x+12 < -8

• 2x + 12 < 8 or 2x+12 < -8

4|5x-2|+7>39

• -6/5<x>2

• x=2 or x=-6/5

• x=2 and x=-6/5

• x<-6/5 or x>2

−2|−2r − 4| = -12

• {5,1}

• {-5, -1}

• {-5, 1}

• No Solution

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