Question

in the equation \\(\frac{v}{w} = x + y\\), to solve for \\(v\\), you should:
a. multiply both sides by \\(w\\)
b. subtract \\(y\\) from both sides
c. add \\(y\\) to both sides
d. divide both sides by \\(x\\)

Explanation:

Step1: Recall solving for a variable

To solve for \( v \) in the equation \( \frac{v}{w}=x + y \), we need to isolate \( v \). The current equation has \( v \) divided by \( w \).

Step2: Determine the operation

To isolate \( v \), we can multiply both sides of the equation by \( w \). This is because multiplying both sides by \( w \) will cancel out the division by \( w \) on the left - hand side.
If we multiply both sides by \( w \), we get \( \frac{v}{w}\times w=(x + y)\times w \), which simplifies to \( v = w(x + y) \).
Let's analyze the other options:

• Option b: Subtracting \( y \) from both sides would give \( \frac{v}{w}-y=x \), which does not isolate \( v \).
• Option c: Adding \( y \) to both sides would give \( \frac{v}{w}+y=x + 2y \), which does not isolate \( v \).
• Option d: Dividing both sides by \( x \) would give \( \frac{v}{w\times x}=1+\frac{y}{x} \), which does not isolate \( v \).

Answer:

a. Multiply both sides by \( w \)