Question

solve for u.
$-\frac{1}{5}(10 - 20u) - u = \frac{1}{3}(6u - 12)$
$u = \boxed{\dfrac{\quad}{\quad}}$

Explanation:

Step1: Distribute the fractions

First, distribute \(-\frac{1}{5}\) on the left side and \(\frac{1}{3}\) on the right side:

$$ -\frac{1}{5} \times 10 + \frac{1}{5} \times 20u - u = \frac{1}{3} \times 6u - \frac{1}{3} \times 12 $$

Simplify each term:

$$ -2 + 4u - u = 2u - 4 $$

Step2: Combine like terms

On the left side, combine \(4u - u\):

$$ -2 + 3u = 2u - 4 $$

Step3: Isolate the variable \(u\)

Subtract \(2u\) from both sides:

$$ -2 + 3u - 2u = -4 $$

Simplify:

$$ -2 + u = -4 $$

Then add 2 to both sides:

$$ u = -4 + 2 $$

$$ u = -2 $$

Answer:

\(u = -2\)