Solving Multi-Step Inequalities 24-25

Front

What is a multi-step inequality?

Back

A multi-step inequality is an inequality that requires more than one step to solve, often involving combining like terms, distributing, and isolating the variable.

Front

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

Back

First, distribute: 3x - 6 < 2x + 18. Then, subtract 2x from both sides: x - 6 < 18. Finally, add 6 to both sides: x < 24.

Front

What does the solution x < 24 represent?

Back

It represents all real numbers less than 24.

Front

What is the solution to the inequality 8 + 6x ≥ 7x + 2 - x?

Back

Combine like terms: 8 + 6x ≥ 6x + 2. Subtract 6x from both sides: 8 ≥ 2, which is always true. Therefore, the solution is all real numbers.

Front

What does the inequality x < -4 mean?

Back

It means that x can be any number less than -4, such as -5, -6, or -4.001.

Front

How do you solve the inequality 2(3 - 6x) > 2(-5x - 6)?

Back

Distribute: 6 - 12x > -10x - 12. Add 12x to both sides: 6 > 2x - 12. Add 12 to both sides: 18 > 2x. Finally, divide by 2: 9 > x or x < 9.

Front

What is the solution to the inequality 3(2x - 8) < 6x + 3?

Back

Distribute: 6x - 24 < 6x + 3. Subtract 6x from both sides: -24 < 3, which is always true. Therefore, the solution is all real numbers.

Front

What is the first step in solving a multi-step inequality?

Back

The first step is to simplify both sides of the inequality, which may involve distributing and combining like terms.

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 reverse the inequality sign.

Front

What is the difference between a solution set and a single solution?

Back

A solution set includes all possible solutions to an inequality, while a single solution refers to one specific value that satisfies the inequality.