Absolute value equations COPY

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 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 of the other side of the equation.

Front

What is the solution to the equation |x| = a, where a > 0?

Back

The solutions are x = a and x = -a.

Front

What does it mean if |x| < a?

Back

It means that x is between -a and a, or -a < x < a.

Front

What does it mean if |x| > a?

Back

It means that x is either less than -a or greater than a, or x < -a or x > a.

Front

Solve the equation |x - 3| = 5.

Back

x = 8 or x = -2.

Front

Solve the equation |2x + 1| = 7.

Back

x = 3 or x = -4.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

The inequality sign flips.

Front

If |x| > -5, what can you conclude?

Back

The solution is all real numbers, since absolute values are always non-negative.

Front

What is the solution to the equation |4x - 3| = 17?

Back

x = 5 or x = -3.5.