If 3x – 4 (64 – x) = 10, then the value of x is

Options

A. `-266`
B. 133
C. 66.5
D. 38

Answer

To solve the equation \(3x - 4(64 - x) = 10\), we will follow these steps:

### Step 1: Distribute the -4
First, we need to distribute the -4 across the terms inside the parentheses:
\[ 3x - 4 \cdot 64 + 4 \cdot x = 10 \]
This simplifies to:
\[ 3x - 256 + 4x = 10 \]

### Step 2: Combine like terms
Next, we combine the \(x\) terms:
\[ (3x + 4x) - 256 = 10 \]
This simplifies to:
\[ 7x - 256 = 10 \]

### Step 3: Move the constant to the right side
Now, we will isolate the \(x\) terms by moving -256 to the right side of the equation:
\[ 7x = 10 + 256 \]
This simplifies to:
\[ 7x = 266 \]

### Step 4: Divide both sides by 7
To solve for \(x\), we divide both sides by 7:
\[ x = \frac{266}{7} \]
Calculating this gives:
\[ x = 38 \]

### Final Answer
Thus, the value of \(x\) is \(38\).

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