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

Front

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

Back

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

Front

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

Back

Subtract 4 from both sides: -3x < 6. Then divide by -3 (remember to flip the inequality): x > -2.

Front

How do you solve the inequality: -2x + 7 ≥ 5x - 3?

Back

Add 2x to both sides: 7 ≥ 7x - 3. Then add 3: 10 ≥ 7x. Finally, divide by 7: x ≤ 10/7.

Front

How do you solve the inequality: 3x + 4 < 7x - 5?

Back

Subtract 3x from both sides: 4 < 4x - 5. Then add 5: 9 < 4x. Finally, divide by 4: x > 9/4.

Front

How do you solve the inequality: 2(x + 1) - 3 > 4x + 5?

Back

Distribute: 2x + 2 - 3 > 4x + 5. Simplify: 2x - 1 > 4x + 5. Subtract 2x: -1 > 2x + 5. Finally, subtract 5: -6 > 2x, or x < -3.

Front

How do you solve the inequality: 6 - 2x ≥ 4x + 8?

Back

Add 2x to both sides: 6 ≥ 6x + 8. Subtract 8: -2 ≥ 6x. Finally, divide by 6: x ≤ -1/3.