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

What does the equation |x| = a imply?

Back

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

Front

What is the solution to |x| = 0?

Back

The solution is x = 0.

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.

Front

Solve |x - 3| = 5.

Back

x = 8 or x = -2.

Front

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

Back

Set up two equations: 2x + 4 = 10 and 2x + 4 = -10.

Front

Solve |3n - 1| + 4 = 10.

Back

n = 3 or n = -1.

Front

What is the solution to |x + 2| = -3?

Back

No solution, because absolute values cannot be negative.

Front

How do you isolate the absolute value in an equation?

Back

Subtract or add any constants on the same side of the equation to isolate the absolute value expression.