Find the value of x : `5(x-8)-14(x-11)+8(x-2(3)/(4))=0`

Options

A. 1
B. `9/2`
C. `(-5)/(8)`
D. 92

Answer

To solve the equation \( 5(x-8) - 14(x-11) + 8\left(x - \frac{2 \cdot 3}{4}\right) = 0 \), we will follow these steps:

### Step 1: Expand the equation
We will distribute the terms inside the parentheses.

\[ 5(x - 8) = 5x - 40 \]
\[ -14(x - 11) = -14x + 154 \]
\[ 8\left(x - \frac{2 \cdot 3}{4}\right) = 8\left(x - \frac{6}{4}\right) = 8\left(x - \frac{3}{2}\right) = 8x - 12 \]

Now, substituting these back into the equation gives us:

\[ 5x - 40 - 14x + 154 + 8x - 12 = 0 \]

### Step 2: Combine like terms
Now, we will combine all the \(x\) terms and the constant terms.

\[ (5x - 14x + 8x) + (-40 + 154 - 12) = 0 \]

Calculating the \(x\) terms:

\[ 5x - 14x + 8x = -1x \]

Calculating the constant terms:

\[ -40 + 154 - 12 = 102 \]

So, we have:

\[ -x + 102 = 0 \]

### Step 3: Solve for \(x\)
Now, we will isolate \(x\).

\[ -x = -102 \]

Multiplying both sides by -1 gives:

\[ x = 102 \]

### Final Answer
The value of \(x\) is \(102\).

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