Solving Multi-Step Inequalities with Word Problems

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 operations like addition, subtraction, multiplication, or division.

Front

How do you solve the inequality -3(9 + x) ≥ -21?

Back

First, distribute -3: -27 - 3x ≥ -21. Then, add 27 to both sides: -3x ≥ 6. Finally, divide by -3 (remember to flip the inequality): x ≤ -2.

Front

What does the solution x ≤ -2 mean in a real-world context?

Back

It means that the value of x can be any number less than or equal to -2.

Front

How do you interpret the inequality m - 5 > 10?

Back

To solve, add 5 to both sides: m > 15. This means m must be greater than 15.

Front

What is the solution to the inequality 8x ≥ -32?

Back

Divide both sides by 8: x ≥ -4.

Front

What does the inequality 0.75n + 1.75 ≤ 20 represent in a word problem?

Back

It represents the total cost of a taxi ride, where 1.75 is the base fare and 0.75 is the cost per additional mile, and it must be less than or equal to $20.

Front

What is the maximum speed limit represented by the inequality s ≤ 55?

Back

It means that the speed s must be less than or equal to 55 miles per hour.

Front

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

Back

Identify and isolate the variable by performing inverse operations.

Front

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

Back

The inequality sign flips direction.

Front

How can you check if your solution to an inequality is correct?

Back

Substitute the solution back into the original inequality to see if it holds true.