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

What does the equation |x - a| = b represent?

Back

It represents two possible equations: x - a = b and x - a = -b.

Front

Solve the equation |x - 3| = 0.

Back

x = 3.

Front

What is the solution set for |x + 9| = -5?

Back

No solution, because absolute values cannot be negative.

Front

How do you solve the equation -2|-2r - 4| = -12?

Back

First, divide both sides by -2 to get | -2r - 4 | = 6, then solve for r.

Front

What are the possible solutions for |2x - 3| + 5 = 10?

Back

x = -1 and x = 4.

Front

Order the following numbers from least to greatest: -2, |8|, 5, |-10|, 6.

Back

-2, 5, 6, 8, 10.

Front

What is the absolute value of -7?

Back

| -7 | = 7.

Front

If |x| = 4, what are the possible values of x?

Back

x = 4 or x = -4.

Front

What is the graphical representation of an absolute value function?

Back

It forms a V-shape on the graph, opening upwards.