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 'less than'. For example, x < 5 means x is less than 5.

Front

What does the symbol '>' mean?

Back

The symbol '>' means 'greater than'. For example, x > 3 means x is greater than 3.

Front

How do you solve the inequality -2(x + 2) < 14?

Back

First, distribute -2: -2x - 4 < 14. Then, add 4 to both sides: -2x < 18. Finally, divide by -2 (remember to flip the inequality): x > -9.

Front

What is the solution to the inequality 3x - 2 < 13?

Back

Add 2 to both sides: 3x < 15. Then, divide by 3: x < 5.

Front

How do you interpret the inequality 10 ≥ x - 3?

Back

This means that x - 3 can be at most 10. Adding 3 to both sides gives x ≤ 13.

Front

What is the solution to the inequality 5z - 2z - 2 < 13?

Back

Combine like terms: 3z - 2 < 13. Add 2 to both sides: 3z < 15. Then, divide by 3: z < 5.

Front

How do you solve the inequality -8x < 48?

Back

Divide both sides by -8 (remember to flip the inequality): x > -6.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 4 means x is less than or equal to 4.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 2 means x is greater than or equal to 2.