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 an absolute-value equation?

Back

Isolate the absolute value expression on one 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 is the solution to the equation |x| = 0?

Back

The only solution is x = 0.

Front

What happens if an absolute-value equation equals a negative number?

Back

There are no solutions, as absolute values cannot be negative.

Front

Solve the equation: |−2n| + 10 = −50

Back

No Solution.

Front

Solve the equation: |−4 + 5x| = 16

Back

x = −12/5, x = 4.

Front

Solve the equation: |2x + 9| = 15

Back

x = 3, x = −12.

Front

Solve the equation: |2a + 10| = 6

Back

a = −8, a = −2.