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 denoted as |x|.

Front

What does the equation |x| = a imply when a < 0?

Back

The equation |x| = a has no solution when a is less than zero, because absolute values cannot be negative.

Front

How do you solve the equation |x + 3| = 5?

Back

To solve |x + 3| = 5, set up two equations: x + 3 = 5 and x + 3 = -5. The solutions are x = 2 and x = -8.

Front

What is the first step in solving an absolute value equation?

Back

The first step is to isolate the absolute value expression on one side of the equation.

Front

What does the equation |−2n| + 10 = −50 tell us about solutions?

Back

Since the left side is always non-negative, the equation has no solution.

Front

How do you interpret the solutions of |x| = 4?

Back

The solutions are x = 4 and x = -4, representing two points equidistant from zero.

Front

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

Back

The solutions are x = 5 and x = -3.5.

Front

How do you solve |8 - 4x| = 16?

Back

Set up two equations: 8 - 4x = 16 and 8 - 4x = -16. The solutions are x = -2 and x = 6.

Front

What is the process for solving 8|-2x + 4| = 96?

Back

First, divide both sides by 8 to get |-2x + 4| = 12, then solve |-2x + 4| = 12.

Front

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

Back

It means that there are no values for the variable that can satisfy the equation.