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, where a is a positive number?

Back

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

Front

What is the solution set for the equation |6 - 2k| = 18?

Back

The solution set is k = -6 and k = 12.

Front

How do you interpret the absolute value in the equation |2a - 10| = 6?

Back

You interpret it as two separate cases: 2a - 10 = 6 and 2a - 10 = -6.

Front

What are the solutions to the equation |2a - 10| = 6?

Back

The solutions are a = 8 and a = 2.

Front

What does the expression |x| < a represent?

Back

It represents the set of all x values that are within a distance a from 0 on the number line.

Front

How do you solve the equation −2|−2r − 4| = -12?

Back

First, divide both sides by -2 to get |−2r − 4| = 6, then solve the resulting absolute value equation.

Front

What is the solution set for the equation −2|−2r − 4| = -12?

Back

The solution set is {-3, -1}.

Front

What is interval notation?

Back

Interval notation is a way of writing subsets of the real number line using intervals, such as (a, b) for all numbers between a and b, not including a and b.

Front

How do you express the solution to the inequality x^2 - x - 12 < 0 in interval notation?

Back

The solution in interval notation is (-3, 4).