Absolute Value Equations and Inequalities

Front

What is an absolute value equation?

Back

An absolute value equation is an equation that contains an absolute value expression, which represents the distance of a number from zero on the number line.

Front

How do you isolate the absolute value in an equation?

Back

To isolate the absolute value, perform operations such as addition, subtraction, multiplication, or division on both sides of the equation until the absolute value expression is alone.

Front

What does the inequality |x| < a represent?

Back

The inequality |x| < a represents the set of all x values that are within a distance a from 0, which can be expressed as -a < x < a.

Front

What does the inequality |x| > a represent?

Back

The inequality |x| > a represents the set of all x values that are more than a distance a from 0, which can be expressed as x < -a or x > a.

Front

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

Back

The first step is to isolate the absolute value expression on one side of the inequality.

Front

How do you split an absolute value equation into two cases?

Back

To split an absolute value equation into two cases, set the expression inside the absolute value equal to both the positive and negative values of the other side of the equation.

Front

What is interval notation?

Back

Interval notation is a way of writing subsets of the real number line using intervals, which can include parentheses for open intervals and brackets for closed intervals.

Front

How do you convert an inequality like x ≤ 6 into interval notation?

Back

The inequality x ≤ 6 can be expressed in interval notation as (-∞, 6].

Front

What is the significance of the absolute value bars in an equation?

Back

The absolute value bars indicate that the expression inside can take on both positive and negative values, reflecting the concept of distance from zero.

Front

What is the solution set for the inequality |x + 7| > 1?

Back

The solution set for the inequality |x + 7| > 1 is x < -8 or x > -6.