Solving Absolute Value Equations

Front

What is an absolute value equation?

Back

An absolute value equation is 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

To solve |x| = a, you set up two equations: x = a and x = -a.

Front

What is the first step in solving |6 - 2k| = 18?

Back

The first step is to set up two separate equations: 6 - 2k = 18 and 6 - 2k = -18.

Front

Solve the equation |6 - 2k| = 18.

Back

k = -6, k = 12.

Front

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

Back

It represents the absolute value of v + 8 being equal to 7, since |v + 8| = 7.

Front

How do you isolate the absolute value in the equation |v + 8| - 5 = 2?

Back

Add 5 to both sides to get |v + 8| = 7.

Front

Solve the equation |v + 8| - 5 = 2.

Back

v = -1, v = -15.

Front

What is the general form of an absolute value equation?

Back

The general form is |ax + b| = c, where a, b, and c are constants.

Front

How do you solve |2a - 10| = 6?

Back

Set up two equations: 2a - 10 = 6 and 2a - 10 = -6.

Front

Solve the equation |2a - 10| = 6.

Back

a = 8, a = 2.