Solving Inequalities Review

Front

What is an inequality?

Back

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

Front

What does a closed circle represent on a number line when graphing inequalities?

Back

A closed circle indicates that the number is included in the solution set, meaning the inequality is 'greater than or equal to' (≥) or 'less than or equal to' (≤).

Front

What does an open circle represent on a number line when graphing inequalities?

Back

An open circle indicates that the number is not included in the solution set, meaning the inequality is 'greater than' (>) or 'less than' (<).

Front

How do you represent the inequality for a number that is less than 5?

Back

The inequality is x < 5.

Front

What is the difference between '≤' and '<'?

Back

'≤' means 'less than or equal to', while '<' means 'less than' only, excluding the number itself.

Front

How would you write an inequality for a situation where a person can spend at most $200?

Back

The inequality would be x ≤ 200, where x represents the amount spent.

Front

What is the first step in solving an inequality?

Back

The first step is to isolate the variable on one side of the inequality.

Front

If you multiply or divide both sides of an inequality by a negative number, what happens to the inequality sign?

Back

The inequality sign flips (changes direction).

Front

How do you graph the inequality x + 2 > 4?

Back

First, solve for x: x > 2. Then, graph an open circle at 2 and shade to the right.

Front

What is the solution set for the inequality 3x ≤ 12?

Back

The solution set is x ≤ 4.