Absolute Value Equations/Inequalites

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 represent?

Back

It represents two possible equations: x = a and x = -a, where a is a non-negative number.

Front

What is the solution to the equation |x + 3| = 5?

Back

x + 3 = 5 or x + 3 = -5, leading to x = 2 or x = -8.

Front

How do you solve the inequality |x| < a?

Back

It represents the range -a < x < a.

Front

What does the inequality |x| > a represent?

Back

It represents two intervals: x < -a or x > a.

Front

What is the solution to the equation |2x - 4| = 6?

Back

2x - 4 = 6 or 2x - 4 = -6, leading to x = 5 or x = -1.

Front

What is the graphical representation of |x| ≤ a?

Back

It is represented by a closed interval on the number line from -a to a.

Front

What is the graphical representation of |x| > a?

Back

It is represented by two open intervals: (-∞, -a) and (a, ∞) on the number line.

Front

What is the solution to the inequality |x - 1| ≥ 3?

Back

x - 1 ≥ 3 or x - 1 ≤ -3, leading to x ≥ 4 or x ≤ -2.

Front

What is the definition of an absolute value equation?

Back

An absolute value equation is an equation that contains an absolute value expression, typically in the form |expression| = value.