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 - 4| = 5

Back

x = 9 and x = -1.

Front

What does the equation |a| = b imply?

Back

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

Front

Solve for x: 2|x - 3| + 4 = 12

Back

x = 7 and x = -1.

Front

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

Back

Isolate the absolute value: |x + 2| = 6.

Front

Solve for x: |3x + 1| = 4

Back

x = 1 and x = -rac{5}{3}.

Front

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

Back

The solution set is {0}.

Front

Solve for x: |2x - 3| = 7

Back

x = 5 and x = -2.

Front

What is the graphical representation of an absolute value function?

Back

The graph of an absolute value function is a V-shape, opening upwards.