Question

1. to isolate ( u ) in ( \frac{u + v}{w} = x ), start by:

a. dividing both sides by ( x )

b. adding ( v ) to both sides

c. multiplying both sides by ( w )

d. subtracting ( v ) from both sides

Explanation:

Step1: Identify goal: isolate u

We need to solve $\frac{u+v}{w}=x$ for $u$.

Step2: Eliminate denominator first

The denominator $w$ is attached to $u+v$. To remove it, multiply both sides by $w$:
$$\frac{u+v}{w} \times w = x \times w$$
This simplifies to $u+v = xw$, which is the first logical step to isolate $u$.

Step3: Evaluate other options

• a. Dividing by $x$ would complicate the left side: $\frac{u+v}{wx}=1$, which does not help isolate $u$.
• b. Adding $v$ gives $\frac{u+v}{w}+v = x+v$, which adds unnecessary terms.
• d. Subtracting $v$ gives $\frac{u+v}{w}-v = x-v$, which also does not eliminate the denominator.

Answer:

c. Multiplying both sides by w