Solving Absolute Value Equations and Inequalities

Front

What is an 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 equation |x| = a where a > 0?

Back

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

Front

What is the solution to the equation |−4 + 5x| = 16?

Back

The solutions are x = -12/5 and x = 4.

Front

What does it mean if |x| < a?

Back

It means that x is within a distance of a from zero, or -a < x < a.

Front

What does it mean if |x| > a?

Back

It means that x is more than a distance of a from zero, or x < -a or x > a.

Front

What is the solution to the equation |2x + 9| = 15?

Back

The solutions are x = 3 and x = -12.

Front

What is the result of |x + 9| = -5?

Back

There is no solution, as absolute values cannot be negative.

Front

How do you write an inequality for the graph showing -2 ≤ x ≤ 5?

Back

The inequality is -2 ≤ x ≤ 5.

Front

How do you write an inequality for the graph showing x ≤ -2 or x > 5?

Back

The inequality is x ≤ -2 or x > 5.

Front

What is the graphical representation of |x| = a?

Back

It represents two points on the number line at a and -a.