Absolute Value Equations & Inequalities

| 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

What's a way to define absolute value?

• The value of a number

• The opposite of a number

• The distance of a number from zero

• The multiplicative inverse of a number

What is the reason that absolute value is always written as a positive?

• Absolute value is talking about numbers so it must be positive.

• Absolute value does not always have to be positive.

• Absolute value is like a clock it has only positive numbers.

• Absolute value is talking about distance, distance is always measured by positive numbers.

An extraneous solution is

• not a concern when solving absolute value equations

• an apparent solution that must be rejected because it does not satisfy the original equation

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

Solve for x: 2|x + 9| = 8

• x = -5 or x = -13

• x = -13

• x = -1/2 or x = -17/2

• No Solution

Solve for x: -4|x + 5| + 2 = -126

• x = 26 or x = -36

• x = 27 or x = -37

• x = 123 or x = -133

• No Solution

Solve for x: 3|2x + 13| ≤ 9

• x ≤ -13 or x ≥ -5

• -13 ≤ x ≤ -5

• -11 ≤ x ≤ -2

• No Solution