If `(3x)/(5)=(x+2)/(3)`, what is the value of x?

Options

A. `(1)/(2)`
B. `1`
C. `2`
D. `2(1)/(2)`

Answer

To solve the equation \(\frac{3x}{5} = \frac{x + 2}{3}\), we will follow these steps:

### Step 1: Cross Multiply
We start by cross multiplying to eliminate the fractions:
\[ 3 \cdot (x + 2) = 5 \cdot 3x \]
This simplifies to:
\[ 3(x + 2) = 5(3x) \]

### Step 2: Distribute
Next, we distribute on both sides:
\[ 3x + 6 = 15x \]

### Step 3: Rearrange the Equation
Now, we will rearrange the equation to isolate \(x\). We can subtract \(3x\) from both sides:
\[ 6 = 15x - 3x \]
This simplifies to:
\[ 6 = 12x \]

### Step 4: Solve for \(x\)
Now we can solve for \(x\) by dividing both sides by 12:
\[ x = \frac{6}{12} \]
This simplifies to:
\[ x = \frac{1}{2} \]

### Final Answer
Thus, the value of \(x\) is \(\frac{1}{2}\).

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