## Solving the Equation: (x+2)-(3x+2)=5(x+4)+1

This article will guide you through the process of solving the equation **(x+2)-(3x+2)=5(x+4)+1**. We will break down each step to ensure a clear understanding of the solution.

### Step 1: Simplify Both Sides of the Equation

First, we need to simplify both sides of the equation by removing the parentheses and combining like terms.

**Left Side:**- (x + 2) - (3x + 2) = x + 2 - 3x - 2 = -2x

**Right Side:**- 5(x + 4) + 1 = 5x + 20 + 1 = 5x + 21

Now our simplified equation looks like this: **-2x = 5x + 21**

### Step 2: Isolate the x Term

To solve for 'x', we need to get all the 'x' terms on one side of the equation. Let's subtract '5x' from both sides:

- -2x - 5x = 5x + 21 - 5x
- This simplifies to:
**-7x = 21**

### Step 3: Solve for 'x'

Finally, we can isolate 'x' by dividing both sides of the equation by -7:

- -7x / -7 = 21 / -7
- This gives us:
**x = -3**

### Conclusion

Therefore, the solution to the equation (x+2)-(3x+2)=5(x+4)+1 is **x = -3**.

You can verify this solution by substituting 'x = -3' back into the original equation and checking if both sides are equal.