Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (e.g., <, >, ≤, ≥) to show that one expression is less than, greater than, or equal to another.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left can be greater than or equal to the value on the right.

Front

How do you solve the inequality 4x - 10 ≤ 22?

Back

Add 10 to both sides: 4x ≤ 32. Then divide by 4: x ≤ 8.

Front

What is the solution to the inequality -2x + 3(-4x + 6) ≤ 116?

Back

First, simplify: -2x - 12x + 18 ≤ 116. Combine like terms: -14x + 18 ≤ 116. Subtract 18: -14x ≤ 98. Divide by -14 (flip the inequality): x ≥ -7.

Front

How do you solve the inequality 3 < -5n + 2n?

Back

Combine like terms: 3 < -3n. Divide by -3 (flip the inequality): n < -1.

Front

When do you flip the inequality sign?

Back

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

Front

Do you flip the sign in the inequality -3x + 2 ≤ 22?

Back

Yes, you flip the sign when you isolate x by multiplying or dividing by a negative number.

Front

What is the solution to the inequality 5x + 3 > 18?

Back

Subtract 3 from both sides: 5x > 15. Then divide by 5: x > 3.

Front

What is the solution to the inequality 2x - 4 < 10?

Back

Add 4 to both sides: 2x < 14. Then divide by 2: x < 7.