Solving Inequalities

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 the symbol '≤' represent in an inequality?

Back

The symbol '≤' means 'less than or equal to'.

Front

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

Back

The symbol '≥' means 'greater than or equal to'.

Front

How do you represent a situation where a person can spend no more than a certain amount?

Back

You can represent this situation using an inequality that includes '≤' to indicate that the total cost must be less than or equal to the specified amount.

Front

What is the difference between an open circle and a closed circle on a number line?

Back

An open circle indicates that the number is not included in the solution (used for '>' or '<'), while a closed circle indicates that the number is included (used for '≥' or '≤').

Front

How do you solve the inequality 84 - 4x ≤ 52?

Back

First, isolate the variable: 84 - 52 ≤ 4x, which simplifies to 32 ≤ 4x. Then divide both sides by 4 to get 8 ≤ x, or x ≥ 8.

Front

What is the solution to the inequality 10 - 3x < 16?

Back

First, isolate the variable: 10 - 16 < 3x, which simplifies to -6 < 3x. Then divide both sides by 3 to get -2 < x, or x > -2.

Front

When graphing the inequality x > 8, what type of circle is used?

Back

An open circle is used when graphing x > 8.

Front

When graphing the inequality x ≤ 8, what type of circle is used?

Back

A closed circle is used when graphing x ≤ 8.

Front

What is the first step in solving a linear inequality?

Back

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