## Solving the Equation: 0.8(x-2) + 2.6 = 0.5(7+x)

This article will guide you through the steps of solving the linear equation: **0.8(x-2) + 2.6 = 0.5(7+x)**

### Step 1: Distribute

Begin by distributing the constants on both sides of the equation:

**0.8(x-2)**becomes**0.8x - 1.6****0.5(7+x)**becomes**3.5 + 0.5x**

This gives us the equation: **0.8x - 1.6 + 2.6 = 3.5 + 0.5x**

### Step 2: Combine Like Terms

Next, combine the constant terms on both sides of the equation:

**-1.6 + 2.6 = 1**- This simplifies the equation to:
**0.8x + 1 = 3.5 + 0.5x**

### Step 3: Isolate the x Term

Now, isolate the *x* term by subtracting **0.5x** from both sides:

**0.8x - 0.5x = 0.3x****3.5 + 0.5x - 0.5x = 3.5**- This leaves us with:
**0.3x + 1 = 3.5**

### Step 4: Isolate x

Finally, isolate *x* by subtracting **1** from both sides and dividing by **0.3**:

**0.3x + 1 - 1 = 3.5 - 1****0.3x = 2.5****0.3x / 0.3 = 2.5 / 0.3****x = 8.33 (approximately)**

### Solution

Therefore, the solution to the equation **0.8(x-2) + 2.6 = 0.5(7+x)** is **x = 8.33** (approximately).