Absolute Value Equations & 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 equation |x| = a where a > 0?

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

How do you isolate the absolute value in an equation?

Back

To isolate the absolute value, you need to move all other terms to the opposite side of the equation.

Front

What is the solution to the equation 4|n + 8| = 56?

Back

The solutions are n = 6 and n = -22.

Front

How do you solve the inequality |k| - 6 ≤ -1?

Back

The solution is -5 ≤ k ≤ 5.

Front

What is the solution to the equation |-6x| = 30?

Back

The solutions are x = 5 and x = -5.

Front

How do you solve the inequality 8 + |4v - 7| ≥ 17?

Back

The solutions are v ≤ -1/2 or v ≥ 4.

Front

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

Back

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