Absolute Value Inequalities

Front

What is an absolute value inequality?

Back

An absolute value inequality is an inequality that contains an absolute value expression, which measures the distance of a number from zero on the number line.

Front

How do you solve the inequality |x| < a?

Back

To solve |x| < a, split it into two inequalities: -a < x < a.

Front

How do you solve the inequality |x| > a?

Back

To solve |x| > a, split it into two inequalities: x < -a or x > a.

Front

What does the expression |x - c| = d represent?

Back

The expression |x - c| = d represents two equations: x - c = d and x - c = -d.

Front

What is the solution to the inequality |x + 3| < 5?

Back

The solution is -8 < x < 2.

Front

What is the solution to the inequality |2x - 4| > 6?

Back

The solution is x < -1 or x > 5.

Front

What does it mean if an absolute value inequality has no solution?

Back

It means that there are no values of the variable that satisfy the inequality.

Front

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

Back

Graph the critical points on a number line and shade the appropriate regions based on the inequality.

Front

What is the solution to the equation |x - 1| = 3?

Back

The solution is x = -2 or x = 4.

Front

What is the solution to the inequality 3|x + 2| - 6 < 0?

Back

The solution is -4 < x < -2.