Absolute Value Equations

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always non-negative.

Front

How do you solve an absolute value equation like |x| = a?

Back

Set up two equations: x = a and x = -a.

Front

What is the first step to solve |x + 1| = 4?

Back

Set up 2 equations: x + 1 = 4 and x + 1 = -4.

Front

What is the first step to solve -2|x + 3| = -10?

Back

Divide by -2 on both sides.

Front

What happens when you have an absolute value equation equal to a negative number?

Back

There is no solution, because absolute values cannot be negative.

Front

What is the solution to |x - 3| = 0?

Back

x = 3.

Front

When do you set up two equations in an absolute value equation?

Back

You set up two equations when the absolute value expression is equal to a positive number.

Front

What is the first step to solve |2x - 1| = -5?

Back

No solution, because absolute values cannot equal a negative number.

Front

How do you isolate the absolute value in an equation like |x + 2| + 3 = 4?

Back

Subtract 3 from both sides to isolate the absolute value.

Front

What is the first step to solve |x + 1| = 4?

Back

Set up 2 equations: x + 1 = 4 and x + 1 = -4.