Solve linear inequalities by using multiplication and division

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: Ava has more than twice the number of apples as Evelyn. If Evelyn has -5 apples, how many apples does Ava have?

• Ava has less than 2 apples

• Ava has more than -5 apples

• Ava has less than -5 apples

• Ava has 5 apples

Answer explanation

To solve the inequality -2y > 10, divide both sides by -2. Remember to flip the inequality sign when dividing by a negative number. Therefore, y < -5 is the correct choice.

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.

Using multiplication, solve the inequality: 2a >= 16

• a > 16

• a = 16

• a <= 8

• a >= 8

Answer explanation

To solve the inequality 2a >= 16, divide both sides by 2. This gives a >= 8. Therefore, the correct choice is a >= 8.

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.

Using division, solve the inequality: 2x represents the number of apples Michael has, and it is greater than 10. How many apples does Michael have?

• Michael has more than 5 apples

• Michael has exactly 5 apples

• Michael has less than 5 apples

• Michael has more than 10 apples

Answer explanation

To solve the inequality 2x > 10, divide both sides by 2. This gives x > 5. Therefore, the correct choice is x > 5.

Using division, solve the inequality: -4y <= 16

• y <= -4

• y = 16

• y > 4

• y >= -4

Answer explanation

To solve the inequality -4y <= 16, divide both sides by -4. Remember to flip the inequality sign when dividing by a negative number. The correct choice is y >= -4.

Using division, solve the inequality: 3z < 9

• z < 3

• z = 3

• z > 3

• z < 9

Answer explanation

To solve the inequality 3z < 9, divide both sides by 3. This gives z < 3. Therefore, the correct choice is z < 3.

Using division, solve the inequality: Mia has at least 25 candies and wants to share them equally among her 5 friends. What is the minimum number of candies each friend will get?

• Mia will get 5 candies

• Each friend will get more than 5 candies

• Each friend will get at most 5 candies

• Each friend will get at least 5 candies

Answer explanation

To solve the inequality 5a >= 25, divide both sides by 5. This gives us a >= 5. Therefore, the correct choice is a >= 5.

Using division, solve the inequality: Hannah has 6 apples and wants to share them equally among her friends. How many friends can she share with if each friend gets more than 5 apples?

• William

• Mason

• Hannah

• More than 5 friends

Answer explanation

To solve the inequality -6b > -30, divide both sides by -6. Remember to flip the inequality sign when dividing by a negative number. The correct choice is b < 5.