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 by |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

Solve the equation |2x + 9| = 15.

Back

x = 3 and x = -12.

Front

What does the equation |x - 3| = 0 imply about x?

Back

It implies that x = 3.

Front

How do you interpret the equation |x - a| = b?

Back

It means that x is either a + b or a - b.

Front

Solve for x: |4x - 3| = 17.

Back

x = 5 and x = -3.5.

Front

What is the solution set for the equation -2|-2r - 4| = -12?

Back

The solution set is {-5, 1}.

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

Solve the equation |x - 12| - 3 = 11.

Back

x = -2 and x = 26.

Front

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

Back

Identify the absolute value expression and set it equal to the positive and negative values of the other side.