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, you set up two equations: x = a and x = -a.

Front

What does it mean if |x| = 0?

Back

If |x| = 0, then x must be 0, as the only number with an absolute value of zero is zero itself.

Front

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

Back

a = 8, a = 2.

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

Solve for r: −2|−2r − 4| = -12

Back

r = -5, r = 1.

Front

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

Back

It indicates that the expression inside the absolute value cannot equal the given value, often when the absolute value is set equal to a negative number.

Front

Solve for n: |−2n| + 10 = −50

Back

No Solution.

Front

What is the solution to |x - 3| = 0?

Back

x = 3.

Front

Solve for p: 9|9 - 2p| = 81

Back

p = 0, p = 9.