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

Front

Solve the equation: |x - 4| = 3.

Back

x = 7, x = 1.

Front

What does the equation |a| = b imply?

Back

It implies that a = b or a = -b, where b is a non-negative number.

Front

Solve the equation: |2x + 1| = 5.

Back

x = 2, x = -3.

Front

What is the first step in solving |x + 2| = 6?

Back

Set up two equations: x + 2 = 6 and x + 2 = -6.

Front

Solve the equation: |3x - 9| = 0.

Back

x = 3.

Front

What is the solution set for |x| = 0?

Back

The solution set is {0}.

Front

Solve the equation: |x + 5| = 10.

Back

x = 5, x = -15.

Front

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

Back

It means that the expression inside the absolute value cannot equal the value on the other side of the equation.