Solve the following:
`(5(1-x)+3(1+x))/(1-2x)=8`

Options

A. `x=4`
B. `x=3`
C. `x=2`
D. `x=0`

Answer

To solve the equation \((5(1-x)+3(1+x))/(1-2x)=8\), we will follow these steps:

### Step 1: Identify the condition for the denominator
Before proceeding with the solution, we need to ensure that the denominator is not equal to zero. Thus, we set the condition:
\[ 1 - 2x \neq 0 \]
This implies:
\[ 2x \neq 1 \quad \Rightarrow \quad x \neq \frac{1}{2} \]

### Step 2: Cross-multiply to eliminate the fraction
We can cross-multiply to eliminate the fraction:
\[ 5(1-x) + 3(1+x) = 8(1-2x) \]

### Step 3: Expand both sides
Now, we will expand both sides of the equation:
- Left side:
\[ 5(1-x) + 3(1+x) = 5 - 5x + 3 + 3x = 8 - 2x \]
- Right side:
\[ 8(1-2x) = 8 - 16x \]

### Step 4: Set the expanded equations equal to each other
Now we have:
\[ 8 - 2x = 8 - 16x \]

### Step 5: Simplify the equation
Next, we will simplify the equation by eliminating \(8\) from both sides:
\[ -2x = -16x \]

### Step 6: Rearrange the equation
Now, we will move all terms involving \(x\) to one side:
\[ -2x + 16x = 0 \]
This simplifies to:
\[ 14x = 0 \]

### Step 7: Solve for \(x\)
Now, we divide both sides by \(14\):
\[ x = 0 \]

### Step 8: Verify the solution
Finally, we should verify that our solution does not violate the condition set in Step 1:
Since \(x = 0\) is not equal to \(\frac{1}{2}\), it is a valid solution.

### Final Answer
Thus, the solution to the equation is:
\[ \boxed{0} \]