Solve : `(x)/(7) +x=16`

Answer

To solve the equation \(\frac{x}{7} + x = 16\), we will follow these steps:

### Step 1: Write the equation
We start with the equation:
\[ \frac{x}{7} + x = 16 \]

### Step 2: Find a common denominator
The common denominator for the terms on the left side is 7. We can rewrite \(x\) as \(\frac{7x}{7}\) to have a common denominator:
\[ \frac{x}{7} + \frac{7x}{7} = 16 \]

### Step 3: Combine the fractions
Now, we can combine the fractions on the left side:
\[ \frac{x + 7x}{7} = 16 \]
This simplifies to:
\[ \frac{8x}{7} = 16 \]

### Step 4: Cross-multiply
To eliminate the fraction, we can cross-multiply:
\[ 8x = 16 \times 7 \]

### Step 5: Calculate the right side
Now we calculate \(16 \times 7\):
\[ 16 \times 7 = 112 \]
So we have:
\[ 8x = 112 \]

### Step 6: Solve for \(x\)
Now, divide both sides by 8 to isolate \(x\):
\[ x = \frac{112}{8} \]
Calculating this gives:
\[ x = 14 \]

### Final Answer
Thus, the solution to the equation is:
\[ x = 14 \]

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