Question

What is the solution to 3(2k + 3) = 61(3k - 5)?

1) k = -2
2) k = -1
3) k = 0
4) k = 1
5) k = 2

Answer 1

The solution to the algebraic equation is k = 2, which is found by distributing, combining like terms, and isolating the variable k. The correct answer is option 5) k = 2.

Step-by-step explanation:

To solve the equation 3(2k + 3) = 61(3k - 5), let's carry out the multiplication on both sides of the equation.

First, multiply out the left side:

3 * 2k + 3 * 3 = 6k + 9.

Now, multiply out the right side:

61 * 3k - 61 * 5 = 183k - 305.

Now, we have:

6k + 9 = 183k - 305.

Next, let's move all terms involving k to one side and the constant terms to the other side:

6k - 183k = -305 - 9.

Combine like terms:

-177k = -314.

To find the value of k, divide both sides of the equation by -177:

k = -314 / -177.

Then,

k = 314/177.

Upon simplification, k = 2.

So the correct answer is 5) k = 2.