Question

start on the left side. two groups of (x + 3), divided into two equal groups, is 1 group of (x + 3). record 1 group of (x + 3) on the left side of the equation.
\\(\frac{2(x + 3)}{2} = \frac{18}{2}\\)
\\(\square = ?\\)

Explanation:

Step1: Simplify the right side

We have the equation \(\frac{2(x + 3)}{2}=\frac{18}{2}\). First, simplify both sides by dividing. For the left side, \(\frac{2(x + 3)}{2}\) simplifies to \(x + 3\) (the 2 in the numerator and denominator cancels out). For the right side, \(\frac{18}{2}=9\).

Step2: Solve for x

Now we have the equation \(x + 3=9\). To solve for \(x\), we subtract 3 from both sides. So \(x=9 - 3\).

Step3: Calculate the result

\(9-3 = 6\), so \(x = 6\). But the question here seems to be about the simplified left - hand side after dividing, which is \(x + 3\), and when we simplify \(\frac{2(x + 3)}{2}\), we get \(x + 3\), and \(\frac{18}{2}=9\), so the left - hand side after simplification (the expression in the box) should be equal to 9? Wait, maybe the question is about the value of \(\frac{2(x + 3)}{2}\) which simplifies to \(x + 3\), and since \(\frac{18}{2}=9\), the value of the left - hand side (the boxed expression) is \(x + 3\) and it equals 9. But if we are just looking at the simplification of \(\frac{2(x + 3)}{2}\), it simplifies to \(x+3\), and \(\frac{18}{2}=9\), so the value in the box (the simplified left - hand side) is \(x + 3\) and it is equal to 9. But maybe the question is asking for the value of \(\frac{2(x + 3)}{2}\) which is \(x + 3\), and since \(\frac{18}{2}=9\), the answer for the box is \(x + 3\) (but if we consider the numerical value when solved, and the right - hand side is 9, then the boxed expression is equal to 9). Wait, let's re - examine. The original equation is \(\frac{2(x + 3)}{2}=\frac{18}{2}\). When we simplify \(\frac{2(x + 3)}{2}\), we get \(x + 3\), and \(\frac{18}{2}=9\). So the left - hand side after simplification (the expression in the box) is \(x + 3\) and it equals 9. But if we are just to find the value of \(\frac{2(x + 3)}{2}\) which is the same as \(x + 3\), and since \(\frac{18}{2}=9\), the value is 9.

Answer:

The value in the box (the simplified left - hand side) is \(x + 3\) (or 9, depending on the context, but if we consider the simplification of \(\frac{2(x + 3)}{2}\), the result is \(x + 3\) and it equals 9). If we are looking for the numerical value of the simplified left - hand side (after the division), it is 9.