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 - 3| = 5?

Back

x = 8 and x = -2.

Front

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

Back

It represents the distance of 2x - 3 from 0, shifted up by 5, equaling 10.

Front

How do you isolate the absolute value in an equation?

Back

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

Front

What is the first step in solving |4x - 3| = 17?

Back

Set up two equations: 4x - 3 = 17 and 4x - 3 = -17.

Front

What is the solution to the equation |x - 6| + 4 = 10?

Back

x = 12 and x = 0.

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.

Front

How do you graph an absolute value function?

Back

The graph of an absolute value function forms a V shape, opening upwards or downwards depending on the coefficient.

Front

What is the solution to the equation |8 - 4x| = 16?

Back

x = -2 and x = 6.