Absolute Value Equations Review

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

Solve the equation |x| = 5.

Back

x = 5 or x = -5.

Front

What does the equation |a| = b imply when b < 0?

Back

The equation has no solution because absolute values cannot be negative.

Front

Solve the equation |3x - 4| = 7.

Back

x = 11/3 or x = -1.

Front

What is the first step in solving an absolute value equation?

Back

Isolate the absolute value expression on one side of the equation.

Front

Solve the equation |2x + 1| = 5.

Back

x = 2 or x = -3.

Front

What is the solution to the equation |x + 3| = 0?

Back

x = -3.

Front

Solve the equation 4|x + 1| - 8 = 12.

Back

x = 4 or x = -6.

Front

What does the equation |x/2 + 3| = 6 represent?

Back

It represents two equations: x/2 + 3 = 6 and x/2 + 3 = -6.

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).