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, isolate the absolute value expression and then set up two separate equations: one for the positive case and one for the negative case.

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 the equation |−2r − 1| = 11?

Back

No Solution, because the expression inside the absolute value cannot equal a negative number.

Front

How do you determine if an absolute value equation has a solution?

Back

An absolute value equation has a solution if the expression inside the absolute value can equal the given number or its negative.

Front

What is the solution to the equation |v + 8| − 5 = 2?

Back

The solutions are v = -15 and v = -1.

Front

How do you order numbers that include absolute values?

Back

Calculate the absolute values, then compare the results to order the numbers from least to greatest.

Front

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

Back

No Solution, because the left side cannot equal a negative number.

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.

Front

What is the absolute value of -10?

Back

The absolute value of -10 is 10, denoted as |-10| = 10.