Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does the symbol '≤' represent in inequalities?

Back

The symbol '≤' means 'less than or equal to'.

Front

What does the symbol '≥' represent in inequalities?

Back

The symbol '≥' means 'greater than or equal to'.

Front

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

Back

To solve, isolate x: -4x ≤ 54 - 14; -4x ≤ 40; x ≥ -10.

Front

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

Back

The inequality sign flips when you multiply or divide both sides by a negative number.

Front

How do you represent a range of values in an inequality?

Back

A range of values can be represented using compound inequalities, such as 2 ≤ x ≤ 8.

Front

What is the solution to the inequality 10 ≥ x - 3?

Back

The solution is x ≤ 13.

Front

What is the first step in solving the inequality 3(x - 2) < 2(x + 9)?

Back

Distribute both sides: 3x - 6 < 2x + 18.

Front

What is the final solution to the inequality 3(x - 2) < 2(x + 9)?

Back

The final solution is x < 24.

Front

What is a compound inequality?

Back

A compound inequality consists of two inequalities joined by 'and' or 'or'.