Absolute Value Equations, Inequalities, and Graphing Review

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 the absolute value equation |x| = a?

Back

To solve |x| = a, you set up two equations: x = a and x = -a.

Front

What is the solution set for the equation |x - 4| = 3?

Back

The solution set is x = 7 and x = 1.

Front

What does the inequality |x| < a represent?

Back

The inequality |x| < a represents the interval -a < x < a.

Front

How do you graph the function y = |x|?

Back

The graph of y = |x| is a V-shaped graph that opens upwards, with the vertex at the origin (0,0).

Front

What is the solution to the inequality |x - 2| > 5?

Back

The solution is x < -3 or x > 7.

Front

How do you interpret the graph of y = -|x|?

Back

The graph of y = -|x| is an upside-down V shape, opening downwards, with the vertex at the origin (0,0).

Front

What is the solution to the equation |2x + 1| = 3?

Back

The solutions are x = 1 and x = -2.

Front

What does the expression |x + 4| = -2 indicate?

Back

The expression |x + 4| = -2 has no solution, as absolute values cannot be negative.

Front

How do you solve the inequality |3x - 1| ≤ 4?

Back

To solve |3x - 1| ≤ 4, set up the compound inequality: -4 ≤ 3x - 1 ≤ 4, leading to the solution x ∈ [-1, 5/3].