If `(6x -1) - (8x - 5) = 7,` then the value of x is ____

Options

A. `-3//2`
B. `3//2`
C. `11//2`
D. `-11//2`

Answer

To solve the equation \( (6x - 1) - (8x - 5) = 7 \), we will follow these steps:

### Step 1: Simplify the left side of the equation
Start by distributing the negative sign in front of the second parentheses:

\[ (6x - 1) - (8x - 5) = 6x - 1 - 8x + 5 \]

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

\[ 6x - 8x + (-1 + 5) = -2x + 4 \]

So the equation now looks like:

\[ -2x + 4 = 7 \]

### Step 3: Isolate the variable term
Next, we want to isolate the term with \( x \). To do this, subtract 4 from both sides:

\[ -2x + 4 - 4 = 7 - 4 \]

This simplifies to:

\[ -2x = 3 \]

### Step 4: Solve for \( x \)
Now, divide both sides by -2 to solve for \( x \):

\[ x = \frac{3}{-2} \]

This simplifies to:

\[ x = -\frac{3}{2} \]

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

\[ \boxed{-\frac{3}{2}} \]

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