Question

solve for u.
-2u = \frac{4}{3}(3u + 6) - 2(3 + \frac{5}{2}u)
u =

Explanation:

Step1: Expand the expressions

First, expand $\frac{4}{3}(3u + 6)$ and $2(3+\frac{5}{2}u)$.
$\frac{4}{3}(3u + 6)=\frac{4}{3}\times3u+\frac{4}{3}\times6 = 4u+8$.
$2(3+\frac{5}{2}u)=2\times3 + 2\times\frac{5}{2}u=6 + 5u$.
The original equation $-2u=\frac{4}{3}(3u + 6)-2(3+\frac{5}{2}u)$ becomes $-2u=(4u + 8)-(6 + 5u)$.

Step2: Simplify the right - hand side

Remove the parentheses: $-2u=4u + 8-6 - 5u$.
Combine like terms on the right - hand side: $-2u=(4u-5u)+(8 - 6)$, so $-2u=-u + 2$.

Step3: Isolate the variable $u$

Add $u$ to both sides of the equation: $-2u+u=-u + 2+u$.
This gives $-u=2$.

Step4: Solve for $u$

Multiply both sides by $- 1$: $(-1)\times(-u)=(-1)\times2$.
So $u=-2$.

Answer:

$-2$