## Solving the Equation (x+2)/5 = (10-2x)/3

This article will guide you through the steps of solving the equation **(x+2)/5 = (10-2x)/3**. We will use the principles of algebraic manipulation to isolate *x* and find its value.

### 1. Eliminate Fractions

To get rid of the fractions, we multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 15.

**15 * [(x+2)/5] = 15 * [(10-2x)/3]**

This simplifies to:

**3(x+2) = 5(10-2x)**

### 2. Expand the Equation

Now, we distribute the constants on both sides of the equation:

**3x + 6 = 50 - 10x**

### 3. Combine Like Terms

Move all *x* terms to one side and all constant terms to the other side:

**3x + 10x = 50 - 6****13x = 44**

### 4. Isolate *x*

Finally, divide both sides by 13 to isolate *x*:

**x = 44/13**

### Solution

Therefore, the solution to the equation **(x+2)/5 = (10-2x)/3** is **x = 44/13**.