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 the equation |x| = a?

Back

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

Front

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

Back

If an absolute value equation has no solution, it means that there is no value of the variable that can satisfy the equation, often because the absolute value cannot equal a negative number.

Front

Solve the equation |x - 3| = 5.

Back

x - 3 = 5 or x - 3 = -5, which gives x = 8 or x = -2.

Front

What is the first step in solving |2x + 4| = 10?

Back

The first step is to set up two separate equations: 2x + 4 = 10 and 2x + 4 = -10.

Front

Solve for x: |x + 1| = 3.

Back

x + 1 = 3 or x + 1 = -3, which gives x = 2 or x = -4.

Front

What is the solution to |x - 2| = -4?

Back

No solution, because absolute values cannot be negative.

Front

If |x + 2| = 6, what are the possible values of x?

Back

x + 2 = 6 or x + 2 = -6, which gives x = 4 or x = -8.

Front

Solve for k: |3k - 9| = 0.

Back

3k - 9 = 0, which gives k = 3.

Front

What does the equation |x| = 0 imply?

Back

It implies that x = 0, as the only number with an absolute value of zero is zero itself.