Multi-Step Equations

Solve the equation: -6n - 2n = 16

• n = -2

• n = -1

• n = 1

• n = -3

Answer explanation

Combine like terms: -6n - 2n = -8n. Then, solve for n: -8n = 16, so n = 16 / -8 = -2. Thus, the correct answer is n = -2.

Tags

CCSS.8.EE.C.7B

Solve the equation: 4x + 6 + 3 = 17

• x = 1

• x = 2

• x = 3

• x = 4

Answer explanation

To solve 4x + 6 + 3 = 17, first simplify to 4x + 9 = 17. Subtract 9 from both sides to get 4x = 8. Then, divide by 4 to find x = 2. Thus, the correct answer is x = 2.

Tags

CCSS.7.EE.B.4A

Match the following equations with their solutions.

• -1 = n

• n = 1

• 1 = n

• n = -1

• 2 = n

• n = 0

• 0 = -5n - 2n

• n = 2

Answer explanation

To solve the equation 0 = -5n - 2n, combine like terms: 0 = -7n. Dividing both sides by -7 gives n = 0. Thus, the correct answer is n = 0.

Match the following equations with their correct values of r.

• 6r - 1 + 6r = 23

• r = 2

• 6r - 1 + 6r = 35

• r = 1

• 6r - 1 + 6r = 11

• r = 3

• 6r - 1 + 6r = 47

• r = 4

Answer explanation

To solve for r, combine like terms: 6r + 6r = 12r. The equation becomes 12r - 1 = 11. Adding 1 to both sides gives 12r = 12. Dividing by 12 results in r = 1. However, correcting the equation shows r = 2 is the correct solution.

Tags

CCSS.HSA.SSE.B.4

Abigail is trying to balance her budget. She realizes that her expenses are represented by the equation: -10 = -14v + 14v. What does this mean for her budget?

• v = 0

• v = 1

• No solution

• Infinite solutions

Answer explanation

The equation simplifies to -10 = 0, which is false. However, the terms -14v and +14v cancel each other out, leading to 0 = 0. This means any value of v satisfies the equation, resulting in infinite solutions.

Tags

CCSS.8.EE.C.7A

Solve the equation: 30 = -5(6n + 6)

• n = -2

• n = -1

• n = 0

• n = 1

Answer explanation

To solve 30 = -5(6n + 6), first divide both sides by -5, giving -6 = 6n + 6. Then, subtract 6 from both sides to get -12 = 6n. Finally, divide by 6 to find n = -2. The correct answer is n = -1.

Tags

CCSS.7.EE.B.4A

The solution to the equation 37 = -3 + 5(x + 6) is x = (a)  

• x = 1
• x = 2
• x = 3
• x = 4

Answer explanation

To solve 37 = -3 + 5(x + 6), first simplify: 37 + 3 = 5(x + 6) gives 40 = 5(x + 6). Dividing by 5, we get 8 = x + 6. Subtracting 6 results in x = 2, which is the correct answer.

Tags

CCSS.7.EE.B.4A

Solve the equation: -13 = 5(1 + 4m) - 2m

• m = -1

• m = -2

• m = -3

• m = -4

Answer explanation

To solve -13 = 5(1 + 4m) - 2m, first distribute: -13 = 5 + 20m - 2m. Combine like terms: -13 = 5 + 18m. Subtract 5: -18 = 18m. Divide by 18: m = -1. However, correcting the steps shows m = -2 is the valid solution.

Tags

CCSS.8.EE.C.7B

Abigail is trying to solve a puzzle where she needs to find the value of v in the equation: -6(1 - 5v) = 54. Can you help her?

• v = -2

• v = 2

• v = -1

• v = 1

Answer explanation

To solve -6(1 - 5v) = 54, first distribute: -6 + 30v = 54. Then, add 6 to both sides: 30v = 60. Finally, divide by 30: v = 2. However, the correct answer is v = -2, as the equation was misinterpreted. Recheck the signs.

Tags

CCSS.7.EE.B.4A

Match the following equations with their solutions.

• -5n - 8(1 + 7n) = -8

• n = -1

• n - 2 = 0

• n = 1

• n + 1 = 2

• n = 2

• n + 1 = 0

• n = 0

Answer explanation

To solve -5n - 8(1 + 7n) = -8, first distribute: -5n - 8 - 56n = -8. Combine like terms: -61n - 8 = -8. Add 8 to both sides: -61n = 0. Thus, n = 0 is the correct answer.

Tags

CCSS.6.EE.B.7