Question

1. solve the equation and check the result

x/5 + 11 = 1/15

2. Verify that x = 8 is a solution of the equation 5x-4/8 - x-3/5 = x+6/5

3. solve : y-1/3 - y-2/4 = 1 and check the result.

Answer 1

1) We are given,

$$\begin{gathered} \frac{x}{5}+11=\frac{1}{15} \\ \Rightarrow \frac{x}{5}=\frac{1}{15}-11 \\ \Rightarrow \frac{x}{5}=\frac{1-165}{15} \\ \Rightarrow x=-\frac{164}{3} \\ \mathrm{Verify}\mathrm{if}\mathrm{LHS}=\mathrm{RHS}. \\ \mathrm{Consider}\mathrm{LHS}=\frac{\mathrm{x}}{5}+11 \\ =\frac{-{\displaystyle \frac{164}{3}}}{5}+11 \\ =\frac{-164}{15}+11 \\ =\frac{-164+165}{15} \\ =\frac{1}{15}=\mathrm{RHS} \\ \mathrm{Hence},\mathrm{verified}\mathrm{LHS}=\mathrm{RHS}. \end{gathered}$$