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

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

Back

The symbol '>' means 'greater than' and indicates that the value on the left is larger than the value on the right.

Front

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

Back

The symbol '<' means 'less than' and indicates that the value on the left is smaller than the value on the right.

Front

How do you represent the solution to the inequality 6 + 2h > 30?

Back

To solve for h, subtract 6 from both sides to get 2h > 24, then divide by 2 to find h > 12.

Front

What does an open circle represent when graphing inequalities?

Back

An open circle is used to indicate that the endpoint is not included in the solution set, typically used with < or >.

Front

What does a closed circle represent when graphing inequalities?

Back

A closed circle indicates that the endpoint is included in the solution set, typically used with ≤ or ≥.

Front

How do you solve the inequality -9x + 7 ≥ 25?

Back

Subtract 7 from both sides to get -9x ≥ 18, then divide by -9 (remember to flip the inequality sign) to find x ≤ -2.

Front

What is the first step to write an inequality for Sam's laptop purchase?

Back

Identify the total amount Sam needs to earn, which is $550, and express it as an inequality based on his hourly wage.

Front

If Sam earns $10.25 per hour, how do you express the inequality for hours worked?

Back

The inequality is 10.25h ≥ 550, where h is the number of hours Sam needs to work.

Front

What is the solution to the inequality 10.25h ≥ 550 when rounded to the next higher hour?

Back

Sam needs to work at least 54 hours.