Solve for k. 8k + 2m = 3m +
The correct answer and explanation is:
Let’s start by solving the equation for kk:
Given:
8k+2m=3m8k + 2m = 3m
Step 1: Subtract 2m2m from both sides to isolate the term with kk
8k=3m−2m8k = 3m – 2m
Step 2: Simplify the right-hand side
8k=m8k = m
Step 3: Divide both sides by 8 to solve for kk
k=m8k = \frac{m}{8}
✅ Final Answer:
k=m8\boxed{k = \frac{m}{8}}
✍️ Explanation (300 words):
To solve the equation 8k+2m=3m8k + 2m = 3m, we aim to isolate the variable kk on one side of the equation. This process is known as solving for a variable, and it’s a fundamental technique in algebra that allows us to express one variable in terms of others.
We begin with the equation: 8k+2m=3m8k + 2m = 3m
Our first step is to move all the terms involving variables other than kk to the opposite side. In this case, the term +2m+2m is on the same side as 8k8k, and we want to remove it from that side to isolate 8k8k. We do that by subtracting 2m2m from both sides: 8k+2m−2m=3m−2m8k + 2m – 2m = 3m – 2m
Simplifying both sides gives: 8k=m8k = m
Now, we have an equation where 8k8k equals mm. To solve for kk, we divide both sides of the equation by 8. Division is the inverse of multiplication, so dividing by 8 cancels out the 8 that’s multiplying kk: k=m8k = \frac{m}{8}
This is the final expression for kk in terms of mm. It tells us that kk is one-eighth of mm. This kind of expression is useful when we know the value of mm and want to calculate kk. The result is linear, meaning it changes proportionally with mm.
Understanding and manipulating equations like this is a key algebra skill used throughout math, science, and engineering.