Solving Absolute Value Equations and Inequalities Review

Front

Define 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

What is the general form of an absolute value equation?

Back

An absolute value equation is typically in the form |A| = B, where A is an expression and B is a non-negative number.

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 does it mean if an absolute value equation has no solution?

Back

An absolute value equation has no solution if the expression inside the absolute value cannot equal a negative number.

Front

Back

x = 8 or x = -2.

Front

What is the solution set for the inequality |x| < a?

Back

The solution set is -a < x < a.

Front

How do you graph the solution of an absolute value inequality?

Back

Graph the critical points on a number line and shade the region that satisfies the inequality.

Front

Back

x = 3 or x = -4.

Front

What is the difference between |A| < B and |A| > B?

Back

|A| < B means A is between -B and B, while |A| > B means A is less than -B or greater than B.

Front

Back

x < -7 or x > -1.