Give step-by-step solution with explanation and final answer:
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Question

VIPSolutions · Accepted Answer

# Step-by-Step Solution

**Problem:**  
Solve for $ x $:  
$ 2(x - 3) = 3(x + 2) - x $

## Step 1: Expand Both Sides

Expand the left and right sides:

Left:  
$ 2(x - 3) = 2x - 6 $

Right:  
$ 3(x + 2) - x = 3x + 6 - x = 2x + 6 $

So the equation becomes:  
$ 2x - 6 = 2x + 6 $

## Step 2: Get All Terms with $ x $ on One Side

Subtract $ 2x $ from both sides:

$ 2x - 6 - 2x = 2x + 6 - 2x $  
$ -6 = 6 $

## Step 3: Analyze the Result

The equation simplifies to $ -6 = 6 $, which is a contradiction.

## Final Answer

There is **no solution** to the equation $ 2(x - 3) = 3(x + 2) - x $. The equation is inconsistent.

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