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

What does it mean to solve an absolute-value equation?

Back

To solve an absolute-value equation, you must find all values of the variable that make the equation true, considering both the positive and negative scenarios.

Front

What is the first step in solving the equation |x| = a?

Back

The first step is to set up two separate equations: x = a and x = -a.

Front

Solve the equation |−2n| + 10 = −50.

Back

No Solution.

Front

Solve the equation −2|−2r − 4| = −12.

Back

r = −5, r = 1.

Front

Solve the equation |6 − 2k| = 18.

Back

k = −6, k = 12.

Front

Solve the equation 3|−8x| + 8 = 80.

Back

x = −3, x = 3.

Front

Solve the equation |2a − 10| = 6.

Back

a = 8, a = 2.

Front

What is the significance of the equation |x| + c = d?

Back

This equation indicates that the absolute value of x, when increased by c, equals d. It can be solved by isolating the absolute value and setting up two cases.

Front

What happens if the right side of an absolute-value equation is negative?

Back

If the right side is negative, the equation has no solution because absolute values cannot be negative.