Absolute Value Inequalities Review

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 represent the inequality |x - 2| ≤ 3?

Back

This represents the range of values for x that are within 3 units of 2, which can be expressed as -1 ≤ x ≤ 5.

Front

What does the symbol '≥' indicate in an inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value can be either greater than or exactly equal to the number.

Front

What does the symbol '≤' indicate in an inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the value can be either less than or exactly equal to the number.

Front

When solving |x - 5| < 2, what is the first step?

Back

The first step is to split the inequality into two separate inequalities: x - 5 < 2 and x - 5 > -2.

Front

What is the solution set for the inequality |x + 4| > 6?

Back

The solution set is x < -10 or x > 2.

Front

What does it mean if an inequality has a closed dot on a number line?

Back

A closed dot indicates that the endpoint is included in the solution set, meaning the value is part of the solution.

Front

What does it mean if an inequality has an open dot on a number line?

Back

An open dot indicates that the endpoint is not included in the solution set, meaning the value is not part of the solution.

Front

How do you solve the compound inequality |x - 3| ≤ 4?

Back

You rewrite it as two inequalities: -4 ≤ x - 3 ≤ 4, then solve for x to get -1 ≤ x ≤ 7.

Front

What is the difference between 'and' and 'or' in compound inequalities?

Back

'And' means both conditions must be true simultaneously, while 'or' means at least one of the conditions must be true.