Absolute Value Equations and Inequalities

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

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

Back

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

Front

What is the solution to the inequality |x| < a?

Back

The solution to |x| < a is -a < x < a.

Front

What is the solution to the inequality |x| > a?

Back

The solution to |x| > a is x < -a or x > a.

Front

What does an open circle represent on a number line?

Back

An open circle represents that the number is not included in the solution set, used for < and >.

Front

What does a closed circle represent on a number line?

Back

A closed circle represents that the number is included in the solution set, used for ≤ and ≥.

Front

Solve for x: |2x - 3| = 5.

Back

x = 4 or x = -1.

Front

Solve for x: |x + 2| < 3.

Back

-5 < x < 1.

Front

What is the first step in solving |ax + b| = c?

Back

Isolate the absolute value expression to get |ax + b| = c.

Front

How do you graph the solution of |x| < 4?

Back

Draw a number line and shade between -4 and 4 with open circles at -4 and 4.