Question

What is the solution of 7k+2=4k-10

A. k=-12
B. k=-4
C. k=-11/12
D. k=4

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the equation 7k + 2 = 4k - 10, we need to isolate the variable k on one side of the equation.

First, let's gather all k terms on one side by subtracting 4k from both sides:

7k + 2 - 4k = 4k - 10 - 4k

This simplifies to:

3k + 2 = -10

Next, let's isolate the variable k by subtracting 2 from both sides:

3k + 2 - 2 = -10 - 2

This simplifies to:

3k = -12

Finally, to find the solution for k, we divide both sides by 3:

3k/3 = -12/3

This simplifies to:

k = -4

Therefore, the solution to the equation 7k + 2 = 4k - 10 is k = -4.

The correct answer is option D. k = 4.

Answer 2

An office manager spent 650% on a new energy-saving copier that will reduce the monthly electric bill for the office from 112$ to 88$. In how many month's will the copier pay for itself.

D. about 27 months
C. about 26 months
B. about 14 months
A. about 3.25 months

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find out how many months it will take for the copier to pay for itself, we need to calculate the savings per month.

The monthly savings from the new copier is the difference between the old electric bill and the new reduced electric bill:

112$ - 88$ = 24$

Now we need to calculate the cost of the copier. Assuming the 650% spent on the copier is the price of the copier itself, we can set up the equation:

650% of X = 24$

To solve for X (the cost of the copier), we divide both sides by 650% (which is the same as dividing by 6.5):

X = 24$ / 6.5 = 3.69$

Therefore, the cost of the copier is approximately 3.69$.

To calculate how many months it will take for the copier to pay for itself, we divide the cost of the copier by the monthly savings:

3.69$ / 24$ = 0.15375

This means it will take approximately 0.15375 months for the copier to pay for itself.

Rounded to the nearest month, the answer is option A. about 3.25 months.

Answer 4

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

To solve the equation 7k + 2 = 4k - 10, we need to isolate the variable "k" on one side of the equation. Here's how you can do it step-by-step:

Step 1: Simplify both sides of the equation by combining like terms.
7k + 2 = 4k - 10
Subtract 4k from both sides:
7k - 4k + 2 = 4k - 4k - 10
3k + 2 = -10

Step 2: Move the constant term to the other side of the equation.
Subtract 2 from both sides:
3k + 2 - 2 = -10 - 2
3k = -12

Step 3: Solve for k by dividing both sides by the coefficient of k.
Divide both sides by 3:
3k/3 = -12/3
k = -4

Therefore, the solution to the equation 7k + 2 = 4k - 10 is k = -4. Hence, the answer is option D.

Answer 5

[AI-generated answer — Explain Bot]

To find the solution of the equation 7k + 2 = 4k - 10, you need to isolate the variable k on one side of the equation. Here's how you can do it:

1. Start by subtracting 4k from both sides of the equation to get rid of the constant term on the right side:
7k + 2 - 4k = 4k - 10 - 4k

Simplifying this yields:
3k + 2 = -10

2. Next, subtract 2 from both sides to isolate the term with k on the left side:
3k + 2 - 2 = -10 - 2

Simplifying this gives:
3k = -12

3. Finally, divide both sides of the equation by 3 to solve for k:
(3k) / 3 = (-12) / 3

This simplifies to:
k = -12 / 3
k = -4

Therefore, the solution to the equation 7k + 2 = 4k - 10 is k = -4. Hence, the correct answer is option B.