Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols such as <, >, ≤, or ≥.

Front

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

Back

The symbol '<' means 'less than'. It indicates that the value on the left side is smaller than the value on the right side.

Front

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

Back

The symbol '>' means 'greater than'. It indicates that the value on the left side is larger than the value on the right side.

Front

How do you solve the inequality 14x + 12 < 9x - 3?

Back

Subtract 9x from both sides: 5x + 12 < -3. Then subtract 12: 5x < -15. Finally, divide by 5: x < -3.

Front

What is the solution to the inequality 11x + 16 < 43 + 2x?

Back

Subtract 2x from both sides: 9x + 16 < 43. Then subtract 16: 9x < 27. Finally, divide by 9: x < 3.

Front

How do you solve the inequality 3(x - 2) < 2(x + 9)?

Back

Distribute: 3x - 6 < 2x + 18. Subtract 2x: x - 6 < 18. Add 6: x < 24.

Front

What does the solution 'a < -3' indicate in the inequality 4(2a + 3) < 3(a - 1)?

Back

It indicates that the value of 'a' must be less than -3 to satisfy the inequality.

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.

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 does the solution 'x > 5' mean in a real-world context?

Back

It means that the value of 'x' must be greater than 5, which could represent a minimum requirement in a scenario.