Question

Which of the equations has one solution? Select all that apply. *

A. -2(w +2) = -3 - 2w

B. 8k + 38 = -3(-6 - 4k)

C. -4(x + 3) = -12 - 4x

D. 36 - 7y = -7(y - 5)

Answer 1

[AI-generated answer — Bot GPT 3.5]

A. -2(w +2) = -3 - 2w

C. -4(x + 3) = -12 - 4x
D. 36 - 7y = -7(y - 5)

Answer 2

no

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the incorrect response.

The equation that has one solution is D. 36 - 7y = -7(y - 5).

Answer 4

[AI-generated answer — Step-by-Step Bot]

To determine which equations have one solution, we need to simplify each equation and check if both sides of the equation are equal.

Let's solve each equation step-by-step:

A. -2(w +2) = -3 - 2w

Step 1: Distribute the -2 to w and 2:
-2w - 4 = -3 - 2w

Step 2: Combine like terms:
-2w + 2w - 4 = -3

-4 = -3

The equation -4 = -3 is not true, so this equation has no solution. Therefore, it does not have one solution.

B. 8k + 38 = -3(-6 - 4k)

Step 1: Distribute the -3 to -6 and -4k:
8k + 38 = 18 + 12k

Step 2: Move all terms with k to one side of the equation:
8k - 12k = 18 - 38

-4k = -20

Step 3: Divide both sides by -4 to solve for k:
k = -20 / -4

k = 5

The equation has one solution: k = 5.

C. -4(x + 3) = -12 - 4x

Step 1: Distribute the -4 to x and 3:
-4x - 12 = -12 - 4x

Step 2: Combine like terms:
-4x + 4x - 12 = -12

-12 = -12

The equation -12 = -12 is true. Both sides are equal, so this equation has infinite solutions and not one solution.

D. 36 - 7y = -7(y - 5)

Step 1: Distribute the -7 to y and -5:
36 - 7y = -7y + 35

Step 2: Move all terms with y to one side of the equation:
-7y + 7y = 35 - 36

0 = -1

The equation 0 = -1 is not true, so this equation has no solution. Therefore, it does not have one solution.

To summarize, the equation B has one solution: k = 5. The equations A, C, and D have either infinite solutions or no solution.

Answer 5

[AI-generated answer — Explain Bot]

To determine which equation(s) have one solution, we need to solve each equation and see if there is only one value that satisfies it.

Let's solve each equation one by one:

A. -2(w +2) = -3 - 2w

First, let's distribute the -2 on the left side:
-2w - 4 = -3 - 2w

The -2w term cancels out on both sides:
-4 = -3

The equation simplifies to -4 = -3, which is not true. Therefore, equation A does not have a solution.

B. 8k + 38 = -3(-6 - 4k)

First, distribute -3 to the terms inside the parentheses on the right side:
8k + 38 = 18 + 12k

Next, let's group the k terms together by subtracting 12k from both sides:
8k - 12k + 38 = 18

Simplify the k terms:
-4k + 38 = 18

Subtract 38 from both sides:
-4k = 18 - 38
-4k = -20

Divide both sides by -4 to solve for k:
k = -20 / -4
k = 5

The equation simplifies to k = 5. Therefore, equation B has a unique solution.

C. -4(x + 3) = -12 - 4x

First, distribute the -4 on the left side:
-4x - 12 = -12 - 4x

The -4x term cancels out on both sides:
-12 = -12

The equation simplifies to -12 = -12, which is a true statement. Therefore, equation C has infinitely many solutions.

D. 36 - 7y = -7(y - 5)

First, distribute -7 to the terms inside the parentheses on the right side:
36 - 7y = -7y + 35

Next, let's subtract -7y from both sides to group the y terms together:
36 - 7y + 7y = 35

Simplify the y terms:
36 = 35

The equation simplifies to 36 = 35, which is not true. Therefore, equation D does not have a solution.

In conclusion, the equation B. 8k + 38 = -3(-6 - 4k) has one solution.