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(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 on a number line?

Back

It represents all numbers to the left of 24, not including 24 itself.

Front

What is the solution to the inequality 11 > -3y + 2?

Back

The solution is y > -3.

Front

How do you isolate y in the inequality -3y < 9?

Back

Divide both sides by -3, remembering to flip the inequality sign: y > -3.

Front

What does an open circle mean when graphing inequalities?

Back

An open circle indicates that the number is not included in the solution set.

Front

What does a closed circle mean when graphing inequalities?

Back

A closed circle indicates that the number is included in the solution set.

Front

If b < 6, how would you graph this inequality?

Back

You would use an open circle at 6 and shade to the left.

Front

What is the change Eleni received after buying 2 pounds of grapes at $3.49 per pound with a $10 bill?

Back

Eleni received $3.02 in change.

Front

How do you determine the correct letter for the inequality 6 > x?

Back

You would choose the letter that represents values less than 6.