Question

1.1 part 2
score: 12/15 answered: 13/15
question 11
solve the equation for u:
$\frac{1}{3}(r - u)=uj + 4w$
give your answer as an equation. this means your answer should have an = sign.
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Explanation:

Step1: Expand the left - hand side

$\frac{1}{3}(r - u)=\frac{1}{3}r-\frac{1}{3}u$. So the equation becomes $\frac{1}{3}r-\frac{1}{3}u = uj+4w$.

Step2: Get terms with $u$ on one side

Add $\frac{1}{3}u$ to both sides: $\frac{1}{3}r=uj + 4w+\frac{1}{3}u$.

Step3: Factor out $u$ on the right - hand side

$\frac{1}{3}r=u(j + \frac{1}{3})+4w$.

Step4: Isolate $u$

Subtract $4w$ from both sides: $\frac{1}{3}r - 4w=u(j+\frac{1}{3})$. Then divide both sides by $(j + \frac{1}{3})$: $u=\frac{\frac{1}{3}r - 4w}{j+\frac{1}{3}}$. Multiply numerator and denominator by 3 to simplify: $u=\frac{r - 12w}{3j + 1}$.

Answer:

$u=\frac{r - 12w}{3j + 1}$