Absolute Value & 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

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 - 5| = 3?

Back

x = 8 or x = 2.

Front

What does the inequality |x| < a mean?

Back

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

Front

What is the solution to the inequality |x + 2| ≤ 4?

Back

-6 ≤ x ≤ 2.

Front

What does the equation |2x - 1| = 5 represent?

Back

It represents two equations: 2x - 1 = 5 and 2x - 1 = -5.

Front

What is the solution to the equation |3x + 4| = 10?

Back

x = 2 or x = -rac{2}{3}.

Front

What does the inequality |x - 3| > 2 mean?

Back

It means that x is either less than 1 or greater than 5.

Front

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

Back

x ≤ -3 or x ≥ 3.

Front

What is the definition of an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, or equal to the other.