Solving Absolute Value Equations

Front

What is an absolute value equation?

Back

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

Isolate the absolute value expression, then set up two separate equations: one for the positive case and one for the negative case.

Front

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

Back

It means that there are no values that satisfy the equation, often occurring when the expression inside the absolute value cannot equal a negative number.

Front

What does it mean if an absolute value equation has one solution?

Back

It means that there is exactly one value that satisfies the equation, typically when the absolute value equals zero.

Front

What does it mean if an absolute value equation has two solutions?

Back

It means that there are two distinct values that satisfy the equation, usually when the absolute value equals a positive number.

Front

Solve for v: |-6v| - 4 = -4

Back

v = 0 (one solution).

Front

Solve for x: |3x - 6| - 9 = -3

Back

x = 0 and x = 4.

Front

Solve for c: |-5c| = 0

Back

c = 0 (one solution).

Front

Solve for z: 11 = 6|-2z| - 5

Back

z = +4/3 and z = -4/3.

Front

Solve for v: |v + 8| - 5 = 2

Back

v = -1 and v = -15.