Solving Two-Step Inequalities with Multiplication and Division

Solve.

- 8 > 56 - 8b

• b > 8

• b > 7/2

• b < -8

• b > 6

If you divide an inequality with a less than sign by -3, what inequality sign would it change to?

Pick the correct inequality.

• A

• B

• C

• D

Which is a possible solution -8(m + 2) < 4(5 + 2m)

• m = -2

• m = -3

• m = -8

• m > -10

Solve

• z ≤ 1

• z ≤ 6

• z ≤ 9

• z ≤ 27

Using multiplication, solve the inequality: 4z represents the number of apples Luna has, and it should be less than or equal to 20 to stay within her budget.

• Luna can buy 5 or fewer apples

• Luna can buy more than 5 apples

• Luna can buy exactly 5 apples

• Luna can buy 5 or more apples

Answer explanation

To solve the inequality 4z <= 20, divide both sides by 4. This gives z <= 5. Therefore, the correct choice is z <= 5.

This inequality needs to be flipped. Choose the reason why:

Using multiplication, solve the inequality: 3x represents the number of apples Evelyn has. How many apples can Evelyn have if she has less than 15 apples?

• Evelyn can have 5 apples

• Evelyn can have less than 3 apples

• Evelyn can have less than 5 apples

• Evelyn can have more than 5 apples

Answer explanation

To solve the inequality 3x < 15, divide both sides by 3. This gives x < 5. Therefore, the correct choice is x < 5.

Using multiplication, solve the inequality: Anika has 5 times less money than Ava. If Ava has more than $25, how much money does Anika have?

• Anika has $5

• Anika has less than $5

• Anika has more than $5

• Anika has less than $5

Answer explanation

To solve the inequality 5b < -25, divide both sides by 5. This gives b < -5. Therefore, the correct choice is b < -5.

6x + 2 + 6x < 14

Mathematical Equivalence

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