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 an absolute value equation?

Back

To solve an absolute value equation, set the expression inside the absolute value equal to both the positive and negative values of the other side of the equation.

Front

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

Back

x = 8 or x = 2.

Front

What is the solution set for |x| = a, where a > 0?

Back

The solution set is x = a and x = -a.

Front

How do you graph an absolute value function?

Back

An absolute value function has a V-shape graph, opening upwards, with the vertex at the point where the expression inside the absolute value equals zero.

Front

Solve for x: |2x - 3| = 7.

Back

x = 5 or x = -2.

Front

What does the inequality |x| < a represent?

Back

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

Front

Solve for x: |x + 4| > 2.

Back

x < -6 or x > -2.

Front

What is the difference between |x| < a and |x| > a?

Back

|x| < a means x is within a distance a from 0, while |x| > a means x is outside that distance.

Front

Solve for x: |x - 1| + 3 = 5.

Back

x = 3 or x = -1.