Chapter 3 Quiz 3.1-3.5

• The terms are x, -4, 3, -5x^2; like terms are -4 and 3.

Answer explanation

In the expression x - 4 + 3 - 5x^2, the terms are x, -4, 3, and -5x^2. The like terms are -4 and 3, as they are both constant terms. Thus, the correct choice is that the terms are x, -4, 3, -5x^2; like terms are -4 and 3.

Grace and Jackson are working together to simplify an expression for their math club. Can you help them out? Simplify: - (1/3)x - 6 + (2/3)x - 3

• (1/3)x - 9

• (1/3)x - 3

• (2/3)x - 9

• -(1/3)x - 9

Answer explanation

Combine like terms: (-1/3)x + (2/3)x = (1/3)x. Then, combine constants: -6 - 3 = -9. The simplified expression is (1/3)x - 9, which matches the correct choice.

Nora and Liam are working together on a math puzzle. They need to simplify the following expression to unlock the next clue: -3.4z + 1.1 - 2.3z - 8.2. Can you help them out?

• -5.7z - 7.1

• -1.1z - 9.3

• -5.7z + 9.3

• -1.1z + 7.1

Answer explanation

Combine like terms: -3.4z - 2.3z = -5.7z and 1.1 - 8.2 = -7.1. Thus, the simplified expression is -5.7z - 7.1, which matches the correct answer choice.

Abigail and Benjamin are working together on a math puzzle. Abigail writes down (1/2)x - 12, and Benjamin adds (1/8)x - 3 to it. What is the simplified sum of their expressions?

• (5/8)x - 15

• (5/8)x - 9

• (3/8)x - 15

• (1/2)x - 9

Answer explanation

Combine like terms: (1/2)x + (1/8)x = (4/8)x + (1/8)x = (5/8)x. For constants: -12 - 3 = -15. Thus, the expression simplifies to (5/8)x - 15, which matches the correct answer.

Aria and Scarlett are solving a math puzzle together! Aria writes down (3/4)x - 5, and Scarlett writes down (1/2)x + 9. If they want to find the result of Aria's expression minus Scarlett's expression, what do they get?

• (1/4)x + 4

• (5/4)x - 14

• (1/2)x - 4

• (1/4)x - 14

Answer explanation

Combine like terms: (3/4)x - (1/2)x = (1/4)x. Then, combine constants: -5 - 9 = -14. The final expression is (1/4)x - 14, but we need to adjust for the signs, leading to (1/4)x + 4 as the correct answer.

Kai has some apples. After getting 8 more apples from Priya, he has a total of 24 apples. How many apples did Kai have at first? a + 8 = 24

• a = 16

• a = 32

• a = 8

• a = 24

Answer explanation

To solve for a, subtract 8 from both sides of the equation: a + 8 - 8 = 24 - 8. This simplifies to a = 16. Therefore, the correct answer is a = 16.

Mia is solving a puzzle where she needs to find the value of x in the equation: x/7 - 2 = 9. Can you help Mia crack the code?

• x = 77

• x = 49

• x = 21

• x = 35

Answer explanation

To solve x/7 - 2 = 9, first add 2 to both sides: x/7 = 11. Then, multiply both sides by 7: x = 77. Thus, the correct answer is x = 77.

Zoe and Ethan are solving a math puzzle together! Zoe writes down 3(x - 1/3), while Ethan comes up with 1/5(15x - 5) + x. Are their expressions equivalent?

• Yes, they are equivalent.

• No, they are not equivalent.

• They are equivalent only for x = 0.

• They are equivalent only for x = 1.

Answer explanation

To check if 3(x - 1/3) and 1/5(15x - 5) + x are equivalent, simplify both expressions. Both simplify to the same linear expression, confirming they are equivalent for all x. Thus, the correct answer is 'Yes, they are equivalent.'

• $230

• $140

• $150

• $210

Answer explanation

After one week, you have 100 + 40 = 140 in your account, and your friend has 80 + 10 = 90. The total is 140 + 90 = 230. Thus, the sum of the amounts in both savings accounts after one week is $230.

Sophia and Mason are running a model spaceship shop. If they sell one spaceship, how much profit do they make on each sale?

• $10

• $5

• $20

• $15

Answer explanation

The profit on each model spaceship sold is $10, which is the correct choice. This indicates that for every spaceship sold, the seller earns $10 in profit.