Chapter 5.5: Absolute Value Equations and Inequalities

Front

What is the absolute value of a number?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always non-negative.

Front

How do you solve an absolute value equation?

Back

To solve an absolute value equation, split it into two separate equations: one for the positive case and one for the negative case.

Front

What does the equation |x| = a represent?

Back

The equation |x| = a represents two solutions: x = a and x = -a, where a is a non-negative number.

Front

What is the first step in solving |x + 3| = 5?

Back

The first step is to split the equation into two cases: x + 3 = 5 and x + 3 = -5.

Front

What are the solutions to the equation |x - 2| = 4?

Back

The solutions are x = 6 and x = -2.

Front

How do you graph an absolute value inequality?

Back

To graph an absolute value inequality, first solve the corresponding absolute value equation, then determine the intervals based on the inequality sign.

Front

What does the inequality |x| < a mean?

Back

The inequality |x| < a means that x is within a distance of a from zero, resulting in the interval -a < x < a.

Front

What does the inequality |x| > a mean?

Back

The inequality |x| > a means that x is outside the distance of a from zero, resulting in the intervals x < -a or x > a.

Front

How do you write the solution for |x + 1| < 3?

Back

The solution is -4 < x < 2.

Front

What is the difference between 'AND' and 'OR' in inequalities?

Back

'AND' means both conditions must be true simultaneously, while 'OR' means at least one condition must be true.