Solving Absolute Value Equations

Front

What is an absolute value equation?

Back

An equation that contains an absolute value expression, which represents the distance of a number from zero on the number line.

Front

How do you solve the equation |x| = a?

Back

Split the equation into two cases: x = a and x = -a.

Front

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

Back

x = 3 or x = -12.

Front

What is the first step in solving |v + 8| - 5 = 2?

Back

Add 5 to both sides to isolate the absolute value: |v + 8| = 7.

Front

Solve the equation |−8x| = 24.

Back

x = -3 or x = 3.

Front

What does the equation |x - 4| = 0 imply?

Back

x = 4, since the absolute value is zero only when the expression inside is zero.

Front

How do you interpret the solution set of an absolute value equation?

Back

The solution set includes all values that satisfy the equation, often resulting in two solutions.

Front

Solve the equation 3|−8x| + 8 = 80.

Back

x = -3 or x = 3.

Front

What is the significance of the absolute value in equations?

Back

It indicates that the expression can be either positive or negative, reflecting distances.

Front

Solve the equation |−4 + 5x| = 16.

Back

x = 4 or x = -12/5.