Solve the Rational Equation: Finding X in (6+x)/(x+5) = 4/11

To solve the given equation $\frac{6+x}{x+5}=\frac{4}{11}$, follow these steps:

• Step 1: Use cross-multiplication to eliminate the fractions. Multiply $11(6 + x)$ and $4(x + 5)$ across the equation:

$11(6 + x) = 4(x + 5)$

• Step 2: Expand both sides of the equation:

$66 + 11x = 4x + 20$

• Step 3: Isolate $x$ by first eliminating the smaller $x$ term. Subtract $4x$ from both sides:

$66 + 11x - 4x = 20$

$66 + 7x = 20$

• Step 4: Further simplify to isolate $x$. Subtract 66 from both sides:

$7x = 20 - 66$

$7x = -46$

• Step 5: Solve for $x$ by dividing both sides by 7:

$x = \frac{-46}{7}$

$x = -6.57$

Therefore, the solution to the equation is \textbf{\( x = -6.57 } \).