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, set the expression inside the absolute value equal to both the positive and negative values of the other side of the equation.

Front

Solve |2a + 10| = 6.

Back

a = -8, a = -2.

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, often because the absolute value cannot equal a negative number.

Front

Solve −2|−2r − 4| = −12.

Back

r = -5, r = 1.

Front

What is the first step in solving |x| = a where a > 0?

Back

Set up two equations: x = a and x = -a.

Front

Solve |2a - 10| = 6.

Back

a = 8, a = 2.

Front

What is the solution set for |−2n| + 10 = −50?

Back

No Solution.

Front

Solve |2x + 9| = 15.

Back

x = 3, x = -12.

Front

What is the significance of the absolute value in equations?

Back

It indicates that the expression can be either positive or negative, leading to two possible equations.