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 is the solution to the equation |2x - 3| + 5 = 10?

Back

The solutions are x = -1 and x = 4.

Front

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

Back

It means that there are no values of x that satisfy the equation, often occurring when the expression inside the absolute value cannot equal a negative number.

Front

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

Back

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

Front

How do you graph an absolute value function?

Back

An absolute value function has a V-shape graph, opening upwards, with the vertex at the point where the expression inside the absolute value equals zero.

Front

What is the general form of an absolute value equation?

Back

The general form is |ax + b| = c, where a, b, and c are constants.

Front

What is the solution to the equation |x| = 7?

Back

The solutions are x = 7 and x = -7.

Front

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

Back

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