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 in an inequality?

Back

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

Front

What does the symbol '>' mean in an inequality?

Back

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

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 2 means x is less than or equal to 2.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 4 means x is greater than or equal to 4.

Front

How do you solve the inequality: 2x - 7 < 15?

Back

Add 7 to both sides: 2x < 22. Then divide by 2: x < 11.

Front

How do you solve the inequality: 3x + 5 > 10?

Back

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

Front

How do you solve the inequality: 2(x + 3) ≤ 6?

Back

Distribute: 2x + 6 ≤ 6. Subtract 6: 2x ≤ 0. Then divide by 2: x ≤ 0.

Front

How do you solve the inequality: 4 - 3x ≥ 10?

Back

Subtract 4 from both sides: -3x ≥ 6. Divide by -3 (reverse the inequality): x ≤ -2.

Front

How do you solve the inequality: 4(x - 3) ≥ 20?

Back

Distribute: 4x - 12 ≥ 20. Add 12: 4x ≥ 32. Then divide by 4: x ≥ 8.