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 |x + 9| = -5 imply?

Back

This equation has no solution because absolute values cannot be negative.

Front

How do you solve the equation |2x – 3| + 5 = 10?

Back

Subtract 5 from both sides to get |2x – 3| = 5. Then, solve the two cases: 2x – 3 = 5 and 2x – 3 = -5.

Front

What are the solutions to |2x – 3| + 5 = 10?

Back

The solutions are x = -1 and x = 4.

Front

What does the equation |x – 3| = 0 mean?

Back

This means that x is exactly 3, as the absolute value is zero only when the expression inside is zero.

Front

What is the solution to |x – 3| = 0?

Back

The solution is x = 3.

Front

How do you order the numbers -2, |8|, 5, |-10|, 6 from least to greatest?

Back

The ordered numbers are -2, 5, 6, 8, 10.

Front

What is the absolute value of -10?

Back

The absolute value of -10 is 10, denoted as |-10| = 10.

Front

What is the solution set for the equation |x| = 24?

Back

The solution set is {24, -24}.

Front

What is the principle behind solving absolute value equations?

Back

To solve |A| = B, where B is non-negative, set A = B and A = -B.