Absolute Value Equations and Inequalities

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, set the expression inside the absolute value equal to both the positive and negative values of the other side of the equation.

Front

What does the inequality |x| < a represent?

Back

It represents the set of all numbers x that are within a distance a from 0 on the number line.

Front

What does the inequality |x| > a represent?

Back

It represents the set of all numbers x that are more than a distance a from 0 on the number line.

Front

Solve the equation |x - 3| = 5.

Back

x - 3 = 5 or x - 3 = -5; thus, x = 8 or x = -2.

Front

Solve the inequality |2x + 1| ≤ 3.

Back

-3 ≤ 2x + 1 ≤ 3; thus, -4 ≤ 2x ≤ 2, leading to -2 ≤ x ≤ 1.

Front

What is the solution to the inequality |x + 4| > 6?

Back

x + 4 > 6 or x + 4 < -6; thus, x > 2 or x < -10.

Front

What is the solution to the equation |x| = 0?

Back

The solution is x = 0.

Front

How do you graph an absolute value function?

Back

An absolute value function is V-shaped, opening upwards, with the vertex at the point where the expression inside the absolute value equals zero.

Front

What is the relationship between absolute value and distance?

Back

Absolute value measures the distance of a number from zero, which is a fundamental concept in understanding inequalities.