If `( 9 - 3x) - (17 x - 10) = 1 ` then the value of x is

Options

A. 1
B. `-1`
C. `(9)/(10)`
D. `(-9)/(10)`

Answer

To solve the equation \( (9 - 3x) - (17x - 10) = 1 \), we will follow these steps:

### Step 1: Simplify the left side of the equation
Start by distributing the negative sign across the second bracket:

\[ 9 - 3x - 17x + 10 = 1 \]

### Step 2: Combine like terms
Now, combine the constant terms (9 and 10) and the terms with \(x\) (-3x and -17x):

\[ (9 + 10) + (-3x - 17x) = 1 \]

This simplifies to:

\[ 19 - 20x = 1 \]

### Step 3: Isolate the term with \(x\)
Next, we want to isolate the term with \(x\) on one side. To do this, subtract 19 from both sides:

\[ -20x = 1 - 19 \]

This simplifies to:

\[ -20x = -18 \]

### Step 4: Solve for \(x\)
Now, divide both sides by -20 to solve for \(x\):

\[ x = \frac{-18}{-20} \]

This simplifies to:

\[ x = \frac{18}{20} \]

### Step 5: Simplify the fraction
Now, simplify the fraction \( \frac{18}{20} \):

\[ x = \frac{9}{10} \]

Thus, the value of \(x\) is:

\[ x = \frac{9}{10} \]

### Final Answer
The value of \(x\) is \( \frac{9}{10} \).

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