Solving Inequalities

Front

What is an inequality?

Back

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

Front

What does the symbol '≥' mean?

Back

'≥' means 'greater than or equal to'. It indicates that the value on the left is either greater than or equal to the value on the right.

Front

What does the symbol '≤' mean?

Back

'≤' means 'less than or equal to'. It indicates that the value on the left is either less than or equal to the value on the right.

Front

How do you solve the inequality: 10 ≥ x - 3?

Back

Add 3 to both sides: 10 + 3 ≥ x, which simplifies to 13 ≥ x or x ≤ 13.

Front

What is the solution to the inequality: 6 > x?

Back

The solution is x < 6.

Front

When solving inequalities, does the sign flip when multiplying or dividing by a negative number?

Back

Yes, the inequality sign flips when you multiply or divide both sides of an inequality by a negative number.

Front

Solve the inequality: 8y < -40. What is y?

Back

Divide both sides by 8: y < -5.

Front

Solve the inequality: 7(x + 3) < 5x + 13. What is x?

Back

Distribute: 7x + 21 < 5x + 13. Then, subtract 5x from both sides: 2x + 21 < 13. Subtract 21: 2x < -8. Finally, divide by 2: x < -4.

Front

Solve the inequality: 3(x - 2) < 2(x + 9). What is x?

Back

Distribute: 3x - 6 < 2x + 18. Subtract 2x from both sides: x - 6 < 18. Add 6: x < 24.

Front

What is the solution set for the inequality x ≤ 13?

Back

The solution set includes all real numbers less than or equal to 13.