Solving Absolute Value Equations

Front

What is an absolute value equation?

Back

An absolute value equation is an equation that contains an absolute value expression, which represents the distance of a number from zero on the number line.

Front

How do you solve an absolute value equation?

Back

To solve an absolute value equation, you set the expression inside the absolute value equal to both the positive and negative values of the other side of the equation.

Front

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

Back

x = 3 or x = -12.

Front

What does the equation |−4 + 5x| = 16 represent?

Back

It represents two equations: -4 + 5x = 16 and -4 + 5x = -16.

Front

What is the solution to the equation |−4 + 5x| = 16?

Back

x = 4 or x = -rac{12}{5}.

Front

What does the equation -|−2r − 1| = 11 imply?

Back

It implies that there is no solution, as the absolute value cannot be negative.

Front

What is the solution to the equation |2a - 10| = 6?

Back

a = 8 or a = 2.

Front

What is the solution to the equation |-2 - 4n| = 34?

Back

n = -9 or n = 8.

Front

What is the definition of absolute value?

Back

Absolute value is the distance of a number from zero, regardless of direction, denoted by |x|.

Front

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

Back

Identify the absolute value expression and set up two separate equations.