Solving Inequalities

Front

What is an inequality?

Back

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

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left can be greater than or equal to the value on the right.

Front

How do you solve the inequality -2x + 3(-4x + 6) ≤ 116?

Back

First, simplify: -2x - 12x + 18 ≤ 116. Combine like terms: -14x + 18 ≤ 116. Subtract 18 from both sides: -14x ≤ 98. Divide by -14 (remember to flip the inequality): x ≥ -7.

Front

What is the solution to the inequality 0.5(x - 8) < 2?

Back

First, multiply both sides by 2: x - 8 < 4. Add 8 to both sides: x < 12.

Front

How do you solve the inequality 30 + n ≥ 50?

Back

Subtract 30 from both sides: n ≥ 20.

Front

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

Back

Add 2 to both sides: 3x < 15. Divide by 3: x < 5.

Front

How do you solve the inequality -8k - 4 ≤ -60?

Back

Add 4 to both sides: -8k ≤ -56. Divide by -8 (remember to flip the inequality): k ≥ 7.

Front

What is the first step in solving an inequality?

Back

The first step is to isolate the variable on one side of the inequality by performing inverse operations.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign.