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

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

### 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:**- (5x-3)-(2x-4) = 5x - 3 - 2x + 4 =
**3x + 1**

- (5x-3)-(2x-4) = 5x - 3 - 2x + 4 =
**Right side:**- -(x+3)-(x+5)+(x+3) = -x - 3 - x - 5 + x + 3 =
**-x - 5**

- -(x+3)-(x+5)+(x+3) = -x - 3 - x - 5 + x + 3 =

Now our equation looks like this: **3x + 1 = -x - 5**

### Step 2: Isolate the x terms

To isolate the x terms, we need to move all terms with x to one side of the equation. Let's add x to both sides:

**3x + 1 + x = -x - 5 + x****4x + 1 = -5**

### Step 3: Isolate the x term

Next, we need to isolate the x term by moving the constant term to the right side of the equation. Subtract 1 from both sides:

**4x + 1 - 1 = -5 - 1****4x = -6**

### Step 4: Solve for x

Finally, we can solve for x by dividing both sides by 4:

**4x / 4 = -6 / 4****x = -3/2**

### Solution

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