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

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 7 means x is less than or equal to 7.

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.

Front

How do you solve the inequality 5(x - 8) < 5?

Back

First, distribute: 5x - 40 < 5. Then, add 40 to both sides: 5x < 45. Finally, divide by 5: x < 9.

Front

Is x = 9 a solution to the inequality x > 9?

Back

No, x = 9 is not a solution because it does not satisfy the condition of being greater than 9.

Front

How do you solve the inequality -4x + 14 ≤ 54?

Back

Subtract 14 from both sides: -4x ≤ 40. Then, divide by -4 (remember to flip the inequality): x ≥ -10.

Front

What is the solution to the inequality x + 5 ≤ 13?

Back

Subtract 5 from both sides: x ≤ 8.

Front

How do you solve the inequality -20 > 18 + m?

Back

Subtract 18 from both sides: -38 > m, or m < -38.