​please solve ques 10 and 11

Q10. Reduce the equation 3x – 4y + 20 = 0 in to normal form 
 
Q11. Solve the inequality $\frac{x +3}{x -7}\le 0$

Dear Student,
Please find below the solution to the asked query:

$$\begin{gathered} 3\mathrm{x}-4\mathrm{y}+20=0 \\ \Rightarrow -3\mathrm{x}+4\mathrm{y}=20 \\ \mathrm{Divide} \mathrm{by} \sqrt{{\left(-3\right)}^2+4^2}=\sqrt{9+16}=5 \\ \Rightarrow -\frac{3}{5}\mathrm{x}+\frac{4}{5}\mathrm{y}=4 \\ \mathrm{Hence} \mathrm{normal} \mathrm{form} \mathrm{is} \\ \mathbf{xcos\alpha }\mathbf{+}\mathbf{ysin\alpha }\mathbf{=}\mathbf{4} \\ \mathrm{Where} \mathrm{cos\alpha }=-\frac{3}{5} \mathrm{and} \mathrm{sin\alpha }=\frac{4}{5} \mathrm{i}.\mathrm{e}. \mathrm{\alpha } \mathrm{lies} \mathrm{in} \mathrm{second} \mathrm{quadrant}. \\ \frac{\mathrm{x}+3}{\mathrm{x}-7}\le 0 \\ \mathrm{Using} \mathrm{method} \mathrm{of} \mathrm{interval}, \mathrm{we} \mathrm{get} \\ \Rightarrow \left(-\infty \right)+++++\left(-3\right)----\left(7\right)+++++\left(\infty \right) \\ \mathrm{Hence} \mathrm{x}\in [-3,7) \end{gathered}$$

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