Solving Absolute-Value Equations

Front

What is an absolute value?

Back

The absolute value of a number is its distance from zero on the number line, always expressed as a positive number.

Front

Solve the equation: |2x + 9| = 15

Back

x = 3, x = -12

Front

What does the equation |v + 8| - 5 = 2 represent?

Back

It represents a situation where the distance of v + 8 from 0, decreased by 5, equals 2.

Front

Solve for k: |6 - 2k| = 18

Back

k = -6, k = 12

Front

Why is absolute value always positive?

Back

Absolute value is always positive because it represents distance, and distance cannot be negative.

Front

Solve the equation: -|−2r − 1| = 11

Back

No Solution

Front

What are the two cases to consider when solving an absolute value equation?

Back

1. The expression inside the absolute value equals the positive value. 2. The expression inside the absolute value equals the negative value.

Front

If |x| = a, what are the possible values of x?

Back

x = a or x = -a.

Front

Solve the equation: |x - 4| = 3

Back

x = 7 or x = 1.

Front

What is the first step in solving an absolute value equation?

Back

Isolate the absolute value expression on one side of the equation.