Solve the Linear Fraction Equation: (5-x)/8 = (3+x)/2

To solve the equation $\frac{5-x}{8} = \frac{3+x}{2}$, we will follow these steps:

• Step 1: Eliminate the fractions by cross-multiplying.
• Step 2: Simplify the resulting equation.
• Step 3: Solve for $x$.

Let's proceed with each step:

Step 1: Cross-multiply.
Cross-multiplying gives:

$(5 - x) \times 2 = (3 + x) \times 8$

Which simplifies to:

$2(5 - x) = 8(3 + x)$

Step 2: Expand and simplify.
Distribute the constants inside the parentheses:

$10 - 2x = 24 + 8x$

Step 3: Isolate $x$.
Add $2x$ to both sides to bring all terms involving $x$ to one side:

$10 = 24 + 10x$

Subtract 24 from both sides to isolate the term with $x$:

$10 - 24 = 10x$

Simplify:

$-14 = 10x$

Finally, divide both sides by 10 to solve for $x$:

$x = \frac{-14}{10}$

Therefore, the solution to the problem is $x = \frac{-14}{10}$, which corresponds to choice .