Question

solve the equation. what is the value of u? right side of the equation. \\(\frac{1}{2}u + 2 = u + 6\\) \\(\underline{ - \frac{1}{2}u \quad \quad \quad \quad - \frac{1}{2}u}\\) \\(2 = \frac{1}{2}u + 6\\) \\(\underline{ - 6 \quad \quad \quad \quad - 6}\\) \\(\boxed{-4} = \square\\)

Explanation:

Step1: Simplify after subtracting 6

After subtracting 6 from both sides, the left side is -4 and the right side is $\frac{1}{2}u$. So we have $-4 = \frac{1}{2}u$.

Step2: Solve for u

To solve for u, multiply both sides by 2. So $u = -4\times2 = -8$. Wait, but first, let's check the step after subtracting 6. Wait, the equation after subtracting 6: left side 2 - 6 = -4, right side $\frac{1}{2}u + 6 - 6 = \frac{1}{2}u$. So now we have $-4 = \frac{1}{2}u$. Then multiply both sides by 2: $u = -8$. But wait, the question here is what's in the square on the right after subtracting 6? Wait, no, the first part: after subtracting 6, right side is $\frac{1}{2}u$ (since 6 - 6 = 0). Wait, no, original steps:

First, we had $\frac{1}{2}u + 2 = u + 6$. Then subtract $\frac{1}{2}u$ from both sides: $2 = \frac{1}{2}u + 6$. Then subtract 6 from both sides: left side 2 - 6 = -4, right side $\frac{1}{2}u + 6 - 6 = \frac{1}{2}u$. So the right side square should have $\frac{1}{2}u$? Wait, no, maybe the next step is to solve for u. Wait, maybe I misread. Wait, the problem is to find what's in the square after subtracting 6 on the right. Wait, no, after subtracting 6, right side is $\frac{1}{2}u$ (because 6 - 6 cancels). But then to solve for u, we can multiply both sides by 2. Wait, let's re-express:

Equation after subtracting 6: $-4 = \frac{1}{2}u$. Then multiply both sides by 2: $u = -8$. But maybe the square is for $\frac{1}{2}u$? No, wait, the steps:

1. Start with $\frac{1}{2}u + 2 = u + 6$
2. Subtract $\frac{1}{2}u$ from both sides: $2 = \frac{1}{2}u + 6$
3. Subtract 6 from both sides: $2 - 6 = \frac{1}{2}u + 6 - 6$ → $-4 = \frac{1}{2}u$

So the right side square after subtracting 6 is $\frac{1}{2}u$? But then to solve for u, we multiply both sides by 2: $u = -8$. Wait, maybe the question is to find u, but the square is for $\frac{1}{2}u$? No, maybe the problem is that after subtracting 6, the right side is $\frac{1}{2}u$, and then we can solve for u. Wait, perhaps I made a mistake. Let's do it again:

Given $\frac{1}{2}u + 2 = u + 6$

Subtract $\frac{1}{2}u$ from both sides:

$2 = \frac{1}{2}u + 6$

Subtract 6 from both sides:

$2 - 6 = \frac{1}{2}u + 6 - 6$

$-4 = \frac{1}{2}u$

Now, to solve for u, multiply both sides by 2:

$u = -4 \times 2 = -8$

But the square on the right after subtracting 6 is $\frac{1}{2}u$, but maybe the question is to find u. Wait, the original problem says "Solve the equation. What is the value of u?" So let's proceed.

So after getting $-4 = \frac{1}{2}u$, multiply both sides by 2:

$u = -8$

Answer:

The value of u is -8. And the value in the right square after subtracting 6 is $\frac{1}{2}u$, but to solve for u, we get u = -8.