https://file.aiquickdraw.com/mathbot/file/17271874063411dq923gn.jpg

The given equation from the image is:

\[
3 + \frac{3}{2}x + 4 = 4x - \frac{5}{2}x
\]

Let me solve this step-by-step.

### Step 1: Simplify both sides of the equation
On the left-hand side:
\[
3 + 4 = 7
\]
So the equation becomes:
\[
7 + \frac{3}{2}x = 4x - \frac{5}{2}x
\]

### Step 2: Combine like terms on the right-hand side
On the right-hand side, combine \( 4x - \frac{5}{2}x \):
\[
4x = \frac{8}{2}x \quad \text{so} \quad \frac{8}{2}x - \frac{5}{2}x = \frac{3}{2}x
\]
Thus, the equation is now:
\[
7 + \frac{3}{2}x = \frac{3}{2}x
\]

### Step 3: Eliminate \( \frac{3}{2}x \) from both sides
Subtract \( \frac{3}{2}x \) from both sides:
\[
7 + \frac{3}{2}x - \frac{3}{2}x = \frac{3}{2}x - \frac{3}{2}x
\]
This simplifies to:
\[
7 = 0
\]

### Step 4: Analyze the result
The equation \( 7 = 0 \) is a contradiction, meaning there is **no solution** to the given equation. 

This implies that the equation is inconsistent, and there is no value of \( x \) that can satisfy it.

Would you like further details or clarifications?

Here are 5 related questions to expand your understanding:
1. How do we recognize when an equation has no solution?
2. What is the difference between inconsistent and consistent equations?
3. How can we identify contradictions in equations early in the solving process?
4. Are there situations where similar equations do have solutions?
5. How can we use algebraic manipulation to verify our results?

**Tip:** Always verify solutions after solving by substituting values back into the original equation to check for consistency.

Learn how to solve the linear equation 3 + (3/2)x + 4 = 4x - (5/2)x step by step. This problem involves simplifying algebraic expressions and identifying contradictions, making it suitable for Grades 8-10.

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