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 the equation |x - 6| + 4 = 10?

Back

Subtract 4 from both sides to get |x - 6| = 6. Then, solve for x: x - 6 = 6 or x - 6 = -6, giving x = 12 and x = 0.

Front

What is the solution set for the inequality |m - 2| < 8?

Back

The solution is -6 < m < 10.

Front

How do you solve the equation |X/8| = 3?

Back

Multiply both sides by 8 to get |X| = 24. The solutions are X = 24 and X = -24.

Front

What is the solution for the equation |2x + 9| = 15?

Back

The solutions are x = 3 and x = -12.

Front

What does the graph of the inequality -4 < x < 2 represent?

Back

It represents all numbers between -4 and 2, not including -4 and 2.

Front

What is the first step in solving an absolute value equation?

Back

Isolate the absolute value expression on one side of the equation.

Front

What does the notation |x| = a imply?

Back

It implies that x can be either a or -a, provided a is non-negative.

Front

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

Back

It means that x is within a distance of a from 0, or -a < x < a.

Front

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

Back

The solutions are x = 2 and x = -8.