Question

If 6h - 2g = 4g + 3h, in terms of g, h = ?

• A. g
• B. 4g
• C. 2g
• D. 5g
• E. 3g

Hint:

When solving for one variable in terms of another, the process is the same as solving a regular equation. Your goal is to get "variable = ...", where the other side contains only other variables and constants.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This is a basic algebraic manipulation problem. The goal is to solve the given linear equation for the variable \(h\), which means expressing \(h\) in terms of \(g\).
Step 2: Key Formula or Approach:
Use standard algebraic operations (addition, subtraction, multiplication, division) to isolate the variable \(h\) on one side of the equation.
Step 3: Detailed Explanation:
The given equation is: \[ 6h - 2g = 4g + 3h \] First, we want to gather all terms containing \(h\) on one side of the equation and all terms containing \(g\) on the other side.
Subtract \(3h\) from both sides: \[ 6h - 3h - 2g = 4g \] \[ 3h - 2g = 4g \] Now, add \(2g\) to both sides to isolate the \(h\) term: \[ 3h = 4g + 2g \] \[ 3h = 6g \] Finally, divide both sides by 3 to solve for \(h\): \[ h = \frac{6g}{3} \] \[ h = 2g \] Step 4: Final Answer:
In terms of g, h is equal to 2g.