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, you set up two equations: x = a and x = -a.

Front

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

Back

The solution set is x = -2 and x = 26.

Front

How many solutions does the equation |c - 7| = 2 have?

Back

The equation |c - 7| = 2 has two solutions.

Front

What is the first step in solving the equation 8 + 3| -8x | = 80?

Back

First, isolate the absolute value expression: 3| -8x | = 72.

Front

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

Back

It means that there are no values of the variable that can satisfy the equation, often because the absolute value cannot equal a negative number.

Front

How do you interpret the equation -2|-2r - 4| = -12?

Back

First, divide both sides by -2 to simplify: |-2r - 4| = 6.

Front

What are the possible values of x in the equation |x| = 3?

Back

The possible values are x = 3 and x = -3.

Front

What is the solution to the equation |−2n| + 10 = −50?

Back

There is no solution because the left side cannot equal a negative number.

Front

What is the general approach to solving absolute value inequalities?

Back

To solve absolute value inequalities, split them into two cases based on the definition of absolute value and solve each case.