Solving Inequalities

Front

What is an inequality?

Back

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

Front

What does the symbol '≤' mean?

Back

'≤' means 'less than or equal to'. It indicates that a value can be less than or equal to another value.

Front

What does the symbol '≥' mean?

Back

'≥' means 'greater than or equal to'. It indicates that a value can be greater than or equal to another value.

Front

How do you solve the inequality x + 5 ≤ 13?

Back

Subtract 5 from both sides: x ≤ 8.

Front

What is the solution to the inequality 3x ≥ 12?

Back

Divide both sides by 3: x ≥ 4.

Front

When do you flip the inequality sign?

Back

You flip the inequality sign when you multiply or divide both sides by a negative number.

Front

What is the solution to the inequality a > 4?

Back

The solution is all values of a that are greater than 4.

Front

How do you graph the inequality x ≤ 8?

Back

Draw a number line, place a closed circle on 8, and shade to the left.

Front

What does the inequality s < 55 represent in a speed limit context?

Back

It represents that the speed s must be less than 55 miles per hour.

Front

What is the solution to the inequality 77 ≤ 5 + 8n?

Back

Subtract 5 from both sides: 72 ≤ 8n, then divide by 8: 9 ≤ n or n ≥ 9.