Absolute Value Equations

Front

What is the definition of 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, isolate the absolute value expression and then set up two separate equations: one for the positive case and one for the negative case.

Front

Solve for x: |x| = 5

Back

x = 5 or x = -5.

Front

What does the equation |x - 3| = 7 represent?

Back

It represents two equations: x - 3 = 7 and x - 3 = -7, leading to x = 10 and x = -4.

Front

Solve for x: 2|x + 1| = 8

Back

x = 3 or x = -5.

Front

What is the first step in solving |2x - 4| = 6?

Back

Isolate the absolute value: 2x - 4 = 6 or 2x - 4 = -6.

Front

Solve for x: |3x + 2| = 11

Back

x = 3 or x = -rac{13}{3}.

Front

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

Back

The solution set is {0}.

Front

Solve for x: |x - 5| + 3 = 10

Back

x = 8 or x = 2.

Front

What does the equation |x + 4| = 2 mean?

Back

It means x + 4 = 2 or x + 4 = -2, leading to x = -2 or x = -6.