Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols such as <, >, ≤, or ≥.

Front

How do you represent a situation where a person needs to earn at least a certain amount of money?

Back

You can represent this situation using an inequality, where the variable represents the hours worked and the expression represents the total earnings.

Front

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

Back

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

Front

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

Back

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

Front

When graphing the inequality x ≤ 3, what type of dot is used on the number line?

Back

A closed dot is used on the number line to indicate that 3 is included in the solution.

Front

When graphing the inequality x < 5, what type of dot is used on the number line?

Back

An open dot is used on the number line to indicate that 5 is not included in the solution.

Front

What is the solution to the inequality -9x + 7 ≥ 25?

Back

The solution is x ≤ -2.

Front

What happens to the inequality symbol when you multiply or divide both sides by a negative number?

Back

The inequality symbol must be flipped when you multiply or divide both sides by a negative number.

Front

How can you solve the inequality 10.25h ≥ 550?

Back

You can solve it by dividing both sides by 10.25, resulting in h ≥ 54. This means Sam needs to work at least 54 hours.

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.