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 the equation |x| = a?

Back

To solve |x| = a, set up two equations: x = a and x = -a.

Front

What does it mean if |x| = -a?

Back

If |x| = -a, there is no solution because absolute values cannot be negative.

Front

Solve for k: |6 - 2k| = 18

Back

k = -6, k = 12.

Front

What is the first step in solving |v + 8| - 5 = 2?

Back

Add 5 to both sides to isolate the absolute value: |v + 8| = 7.

Front

Solve for v: |v + 8| = 7

Back

v = -1 or v = -15.

Front

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

Back

It indicates that the equation is set up in a way that cannot be satisfied, often due to a negative result from an absolute value.

Front

Solve for n: |-2n| + 10 = -50

Back

No Solution.

Front

How do you interpret |2a - 10| = 6?

Back

Set up two equations: 2a - 10 = 6 and 2a - 10 = -6.

Front

Solve for a: |2a - 10| = 6

Back

a = 8 or a = 2.