Solve for $$ u $$. $$ \begin{array}{l}-2 u=\frac{4}{3}(3 u+6)-2\left(3+\frac{5}{2} u ight) \ u=\square\end{array} $$

Question

Solve for $$ u $$. $$ \begin{array}{l}-2 u=\frac{4}{3}(3 u+6)-2\left(3+\frac{5}{2} uight) \ u=\square\end{array} $$

UpStudy AI · Accepted Answer

To solve for $$ u $$ in the equation:

$$
-2u = \frac{4}{3}(3u + 6) - 2\left(3 + \frac{5}{2}u\right)
$$

**Step 1: Expand and Simplify Both Sides**

First, expand the right-hand side of the equation:

$$
\frac{4}{3}(3u + 6) = \frac{4}{3} \times 3u + \frac{4}{3} \times 6 = 4u + 8
$$

$$
-2\left(3 + \frac{5}{2}u\right) = -2 \times 3 - 2 \times \frac{5}{2}u = -6 - 5u
$$

Now, substitute these back into the original equation:

$$
-2u = 4u + 8 - 6 - 5u
$$

Combine like terms on the right-hand side:

$$
4u - 5u + 8 - 6 = -u + 2
$$

So, the equation simplifies to:

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

**Step 2: Solve for $$ u $$**

To isolate $$ u $$, follow these steps:

1. **Add $$ 2u $$ to both sides:**

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

$$
0 = u + 2
$$

2. **Subtract 2 from both sides:**

$$
0 - 2 = u + 2 - 2
$$

$$
-2 = u
$$

**Solution:**

$$
u = -2
$$
$$ u = -2 $$

Solve for \( u \). \( \begin{array}{l}-2 u=\frac{4}{3}(3 u+6)-2\left(3+\frac{5}{2} u\right) \\ u=\square\end{array} \)