Let's solve the equation:

\[
x - \frac{5}{2} + x + \frac{3}{3} = x - \left( x + \frac{9}{6} \right)
\]

### Step 1: Simplify the equation

\[
x - \frac{5}{2} + x + 1 = x - \left( x + \frac{3}{2} \right)
\]
Since \(\frac{3}{3} = 1\) and \(\frac{9}{6} = \frac{3}{2}\).

### Step 2: Combine like terms

On the left-hand side:
\[
x + x - \frac{5}{2} + 1 = 2x - \frac{5}{2} + 1
\]
On the right-hand side:
\[
x - x - \frac{3}{2} = -\frac{3}{2}
\]

Thus, the equation becomes:
\[
2x - \frac{5}{2} + 1 = -\frac{3}{2}
\]

### Step 3: Combine constants on the left-hand side
First, simplify \( -\frac{5}{2} + 1 \):
\[
-\frac{5}{2} + \frac{2}{2} = -\frac{3}{2}
\]
So the equation becomes:
\[
2x - \frac{3}{2} = -\frac{3}{2}
\]

### Step 4: Isolate \(x\)

Now, add \(\frac{3}{2}\) to both sides:
\[
2x = 0
\]

### Step 5: Solve for \(x\)

Divide both sides by 2:
\[
x = 0
\]

### Solution:
The solution is \(x = 0\).

Would you like more details on any of the steps?

### Related Questions:
1. How would the solution change if the constants were different?
2. Can you apply the same method to solve other linear equations?
3. What if the equation involved higher-degree terms like \(x^2\)?
4. How do you handle equations involving fractions more efficiently?
5. What are the key differences between solving linear and quadratic equations?

### Tip:
Always simplify fractions and combine like terms early to make equations easier to solve.

Learn how to solve the linear equation x - 5/2 + x + 1 = x - (x + 3/2) with a detailed step-by-step solution. This problem covers algebraic concepts such as combining like terms and fraction simplification. Suitable for students in Grades 6-8.

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