Solving Inequalities

Front

What is an inequality?

Back

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

Front

What does the symbol '>' mean?

Back

The symbol '>' means 'greater than'. For example, a > 4 means 'a is greater than 4'.

Front

What does the symbol '<' mean?

Back

The symbol '<' means 'less than'. For example, a < 6 means 'a is less than 6'.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. For example, c ≥ 9 means 'c is greater than or equal to 9'.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. For example, c ≤ 9 means 'c is less than or equal to 9'.

Front

How do you solve the inequality 22 < 6c + 4?

Back

Subtract 4 from both sides: 18 < 6c. Then divide by 6: 3 < c or c > 3.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign.

Front

Solve the inequality -3x ≥ 12. Do you need to flip the sign?

Back

Yes, divide by -3 and flip the sign: x ≤ -4.

Front

How do you graph the inequality c < 9?

Back

Draw a number line, place an open circle at 9, and shade to the left to indicate all numbers less than 9.

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.