Absolute Value

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 equation involving absolute value?

Back

To solve an equation involving absolute value, you set up two separate equations: one for the positive case and one for the negative case.

Front

Solve for x: |x - 6| + 4 = 10.

Back

x = 12 and x = 0.

Front

What is the first step in solving |x + 5| = 3?

Back

Set up two equations: x + 5 = 3 and x + 5 = -3.

Front

Solve for x: -4|x + 5| + 2 = -126.

Back

x = 27 or x = -37.

Front

What does the equation |2x - 3| + 5 = 10 represent?

Back

It represents two cases: 2x - 3 = 5 and 2x - 3 = -5.

Front

Solve for x: |8 - 4x| = 16.

Back

x = -2 and x = 6.

Front

What is the solution set for |x| = a, where a is a positive number?

Back

The solution set is {a, -a}.

Front

Solve for x: 8|-2x + 4| = 96.

Back

x = -4 and x = 8.

Front

What is the graphical representation of absolute value functions?

Back

Absolute value functions create a V-shape on a graph, opening upwards.