Solve for X: Fraction Equation 4/(x+5) = 8/((2-x)×3)

To solve the equation $\frac{4}{x+5} = \frac{8}{(2-x) \times 3}$, we will use cross-multiplication.

• Step 1: Set up the cross-multiplication: $4 \times (2-x) \times 3 = 8 \times (x+5)$
• Step 2: Simplify the left side of the equation: $12(2-x) = 8(x+5)$
• Step 3: Distribute on both sides: $24 - 12x = 8x + 40$
• Step 4: Combine like terms. First, bring all terms involving $x$ to one side and constant terms to the other side: $24 - 40 = 8x + 12x$
• Step 5: Simplify the equation: $-16 = 20x$
• Step 6: Solve for $x$ by dividing both sides by 20: $x = -\frac{16}{20}$
• Step 7: Simplify the fraction: $x = -\frac{4}{5}$

Therefore, the solution to the equation is $x = -\frac{4}{5}$.