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 or equal to'.

Front

What does the symbol '≥' mean?

Back

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

Front

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

Back

First, distribute: 3x - 9 ≤ 2x + 4. Then, isolate x: x ≤ 13.

Front

What is the solution to the inequality -3 + x ≤ -11?

Back

Add 3 to both sides: x ≤ -8.

Front

How do you solve the inequality 0.5(x - 8) < 2?

Back

First, distribute: 0.5x - 4 < 2. Then, isolate x: x < 12.

Front

What is the solution to the inequality -1(2x + 4) ≥ 6?

Back

Distribute: -2x - 4 ≥ 6. Then, isolate x: x ≤ -5.

Front

How do you solve the inequality -2(x + 2) < 14?

Back

Distribute: -2x - 4 < 14. Then, isolate x: x > -9.

Front

What is the importance of reversing the inequality sign?

Back

The inequality sign must be reversed when multiplying or dividing both sides by a negative number.

Front

What is a compound inequality?

Back

A compound inequality combines two inequalities, often using 'and' or 'or'.