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 |x - 5| = 3.

Back

x = 8 or x = 2.

Front

What does the equation |a| = b imply?

Back

It implies that a = b or a = -b, provided b is non-negative.

Front

Solve |2x + 1| = 7.

Back

x = 3 or x = -4.

Front

What is the first step in solving |x + 4| = 10?

Back

Set up two equations: x + 4 = 10 and x + 4 = -10.

Front

Solve |3k - 6| = 12.

Back

k = 6 or k = -2.

Front

What is the solution set for |x| = 0?

Back

The solution set is {0}.

Front

Solve |x - 2| + 3 = 5.

Back

x = 4 or x = 0.

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 solutions.