Absolute Value Equations & 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| < b represent?

Back

It represents the values of x that are within a distance b from a on the number line.

Front

What does the inequality |x - a| > b represent?

Back

It represents the values of x that are more than a distance b from a on the number line.

Front

How do you interpret the solution of |x - 6| < 4?

Back

The solution is 2 < x < 10, meaning x is between 2 and 10.

Front

What is the solution to the equation |5x| = 40?

Back

The solutions are x = 8 and x = -8.

Front

How do you solve the equation 2|x - 4| + 8 = 18?

Back

First, isolate the absolute value: |x - 4| = 5. Then, solve for x: x - 4 = 5 or x - 4 = -5, giving x = 9 and x = -1.

Front

What does the graph of x ≤ -2 OR x > 5 look like?

Back

It includes all values less than or equal to -2 and all values greater than 5 on the number line.

Front

What is the solution to the inequality |x| < 3?

Back

The solution is -3 < x < 3.

Front

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

Back

The solution is x < -4 or x > 4.