Solving Absolute Value Equations

Front

What is an 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?

Back

To solve an absolute value equation |A| = B, you set up two equations: A = B and A = -B.

Front

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

Back

x = 3 or x = -12.

Front

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

Back

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

Front

Solve the equation: |v + 8| - 5 = 2

Back

v = -15 or v = -1.

Front

What is the first step in solving |−2n| + 10 = −50?

Back

Recognize that the left side cannot be negative, so there is no solution.

Front

Solve the equation: |−4 + 5x| = 16

Back

x = -12/5 or x = 4.

Front

What is the significance of the two cases in absolute value equations?

Back

The two cases represent the two possible scenarios: the expression inside the absolute value can be either positive or negative.

Front

Solve the equation: 3|−8x| + 8 = 80

Back

x = -3 or x = 3.

Front

What is the general form of an absolute value equation?

Back

The general form is |A| = B, where A is an expression involving the variable and B is a non-negative number.