Solve :
`(1)/(10)-(7)/(x)=35`

Options

A. `-(70)/(349)`
B. `-(69)/(329)`
C. `-(70)/(369)`
D. `-(70)/(299)`

Answer

To solve the equation \( \frac{1}{10} - \frac{7}{x} = 35 \), we will follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ \frac{1}{10} - \frac{7}{x} = 35 \]

### Step 2: Eliminate the fractions
To eliminate the fractions, we can find a common denominator. The common denominator for \(10\) and \(x\) is \(10x\). We will multiply every term in the equation by \(10x\):
\[ 10x \left(\frac{1}{10}\right) - 10x \left(\frac{7}{x}\right) = 10x \cdot 35 \]

This simplifies to:
\[ x - 70 = 350x \]

### Step 3: Rearrange the equation
Next, we will rearrange the equation to get all \(x\) terms on one side and constants on the other side:
\[ x - 350x = 70 \]
This simplifies to:
\[ -349x = 70 \]

### Step 4: Solve for \(x\)
Now, we will divide both sides by \(-349\) to isolate \(x\):
\[ x = \frac{70}{-349} \]
This simplifies to:
\[ x = -\frac{70}{349} \]

### Final Answer
Thus, the solution to the equation is:
\[ x = -\frac{70}{349} \]

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