Solve : `3.7x+5.2 = 0.3 x +13.7`

Answer

To solve the equation \(3.7x + 5.2 = 0.3x + 13.7\), we will follow these steps:

### Step 1: Rearrange the equation
We want to get all the terms involving \(x\) on one side and the constant terms on the other side. We can do this by subtracting \(0.3x\) from both sides and subtracting \(5.2\) from both sides.

\[ 3.7x - 0.3x + 5.2 - 5.2 = 0.3x - 0.3x + 13.7 - 5.2 \]

### Step 2: Simplify the equation
Now, simplify both sides of the equation.

\[ (3.7 - 0.3)x = 13.7 - 5.2 \]

Calculating the left side:

\[ 3.7 - 0.3 = 3.4 \]

Calculating the right side:

\[ 13.7 - 5.2 = 8.5 \]

So we have:

\[ 3.4x = 8.5 \]

### Step 3: Solve for \(x\)
Now, to find \(x\), we divide both sides of the equation by \(3.4\).

\[ x = \frac{8.5}{3.4} \]

### Step 4: Simplify the fraction
To simplify \(\frac{8.5}{3.4}\), we can multiply the numerator and the denominator by 10 to eliminate the decimal.

\[ x = \frac{85}{34} \]

### Step 5: Final simplification
Now, we can simplify \(\frac{85}{34}\) if possible. Both 85 and 34 can be divided by 17.

\[ x = \frac{85 \div 17}{34 \div 17} = \frac{5}{2} \]

Thus, the solution is:

\[ x = 2.5 \]