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

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 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 an absolute value equation has no solution?

Back

An absolute value equation has no solution if the expression inside the absolute value cannot equal a negative number.

Front

Solve: |x - 5| = 3. What are the solutions?

Back

x = 8 and x = 2.

Front

What is the solution to the equation |−2n| - 30 = −20?

Back

The solutions are n = 5 and n = -5.

Front

Solve: 11 - 8|x - 9| = -29. What are the solutions?

Back

x = 14 and x = 4.

Front

What is the solution to the equation |−2n| + 10 = −50?

Back

No Solution.

Front

Solve: −2|−2r − 4| = -12. What are the solutions?

Back

The solutions are r = -5 and r = 1.

Front

What is the first step in solving the equation 2 - 3|7 - x| = 14?

Back

Isolate the absolute value expression: 3|7 - x| = -12.