Absolute Value Equations

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 absolute value equation of the form |x| = a?

Back

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

Front

What is the solution to the equation |x - 12| - 3 = 11?

Back

The solutions are x = -2 and x = 26.

Front

What does it mean if |x + 9| = -5?

Back

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

Front

How do you isolate the absolute value in an equation?

Back

To isolate the absolute value, add or subtract terms from both sides of the equation until the absolute value expression is alone.

Front

What is the solution to the equation 3|−8x| + 8 = 80?

Back

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

Front

What is the first step in solving the equation 2|x - 4| + 8 = 18?

Back

Subtract 8 from both sides to isolate the absolute value: 2|x - 4| = 10.

Front

What is the solution to the equation |−2n| - 30 = −20?

Back

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

Front

What does the equation |x| = 0 imply about x?

Back

It implies that x = 0, as the only number with an absolute value of zero is zero itself.

Front

How do you graph the absolute value function y = |x|?

Back

The graph is a V-shape that opens upwards, with the vertex at the origin (0,0).