Question

Solve the equation for the designated variable w₁:

R = (wᵢ - wₙ) / 3 * (R - w₂)
Options:
A. R - w₂
B. 3R - w₂
C. 3R + w₂
D. 3 - w₂

Answer 1

To solve the equation R = (wᵢ - wₙ) / 3 * (R - w₂) for the designated variable w₁, you need to isolate w₁ on one side of the equation. Multiply both sides of the equation by 3 to eliminate the fraction, then expand and rearrange the terms. Finally, divide both sides by (R - wᵢ) to solve for w₁.

Step-by-step explanation:

To solve the equation R = (wᵢ - wₙ) / 3 * (R - w₂) for the designated variable w₁, we need to isolate w₁ on one side of the equation.

Step 1: Multiply both sides of the equation by 3 to eliminate the fraction: 3 * R = (wᵢ - wₙ) * (R - w₂).

Step 2: Expand the equation: 3R = wᵢR - wᵢw₂ - wₙR + wₙw₂.

Step 3: Gather the terms containing w₁ on one side: 3R + wᵢw₂ - wₙw₂ = wᵢR - wₙR.

Step 4: Factor out w₁ on the right side: w₁(R - wᵢ) = 3R + wᵢw₂ - wₙw₂.

Step 5: Lastly, divide both sides of the equation by (R - wᵢ) to solve for w₁: w₁ = (3R + wᵢw₂ - wₙw₂) / (R - wᵢ).