Absolute Value Equations Inequalities

−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: 3|2x + 13| ≤ 9

• x ≤ -13 or x ≥ -5

• -13 ≤ x ≤ -5

• -11 ≤ x ≤ -2

• No Solution

Solve for x: 4|3x - 5| + 20 > 6

• 4/3 < x < 2

• x < 4/3 or x > 2

• x > 14/3 or x < -4/3

• No Solution

Solve for x: 0.5|x + 14| - 3 = 7

• x = -6 or x = -22

• x = 6 or x = -34

• x = -9 or x = -19

• 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