QuestionSolving Rational Equations Solve each of the following rational equations algebraically (also called symbolically). Check your work by plugging the value(s) back into the equation or by graphing. Note: You must give each answer as an integer or reduced fraction and written as an equation. $$\begin{array}{c|c} 8=\frac{49}{x-2} & \frac{2}{x+8}=\frac{4}{x-3} \\ \frac{x+10}{2}=\frac{x-1}{6} & 10=2+\frac{11}{x+6} \end{array}$$

Studdy Solution
For the equation $10 = 2 + \frac{11}{x+6}$, first subtract 2 from both sides:
$$8 = \frac{11}{x+6}$$
Multiply both sides by $x+6$ to eliminate the fraction:
$$8(x+6) = 11$$
Expand and simplify:
$$8x + 48 = 11$$
Subtract 48 from both sides:
$$8x = 11 - 48$$ $$8x = -37$$
Divide by 8:
$$x = -\frac{37}{8}$$
The solutions are:
1. $x = \frac{65}{8}$
2. $x = -19$
3. $x = -\frac{31}{2}$
4. $x = -\frac{37}{8}$