Find the value of expression `(x - 6) - (x - 5) + 40 - 17 (x - 2) " at " x = (1)/(17)`

Options

A. 73
B. `-4`
C. 75
D. 72

Answer

To find the value of the expression \((x - 6) - (x - 5) + 40 - 17(x - 2)\) at \(x = \frac{1}{17}\), we will follow these steps:

### Step 1: Substitute \(x\) with \(\frac{1}{17}\)
We start by substituting \(x\) in the expression:
\[ \left(\frac{1}{17} - 6\right) - \left(\frac{1}{17} - 5\right) + 40 - 17\left(\frac{1}{17} - 2\right) \]

### Step 2: Simplify each term
Now we simplify each term inside the expression:
1. \(\frac{1}{17} - 6 = \frac{1 - 102}{17} = \frac{-101}{17}\)
2. \(\frac{1}{17} - 5 = \frac{1 - 85}{17} = \frac{-84}{17}\)
3. \(17\left(\frac{1}{17} - 2\right) = 17\left(\frac{1 - 34}{17}\right) = -33\)

Now, substituting these simplified terms back into the expression:
\[ \frac{-101}{17} - \frac{-84}{17} + 40 - (-33) \]

### Step 3: Combine the terms
Now we combine the terms:
\[ \frac{-101 + 84}{17} + 40 + 33 \]
This simplifies to:
\[ \frac{-17}{17} + 40 + 33 = -1 + 40 + 33 \]

### Step 4: Final Calculation
Now, we calculate:
\[ -1 + 40 + 33 = 72 \]

Thus, the value of the expression at \(x = \frac{1}{17}\) is \(\boxed{72}\).

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