Question

# 1. solve the equation and check the resultx/5 + 11 = 1/152. Verify that x = 8 is a solution of the equation 5x-4/8 - x-3/5 = x+6/53. solve : y-1/3 - y-2/4 = 1 and check the result.

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Solution

## 1) We are given, $\frac{x}{5}+11=\frac{1}{15}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}⇒\frac{x}{5}=\frac{1}{15}-11\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}⇒\frac{x}{5}=\frac{1-165}{15}\phantom{\rule{0ex}{0ex}}⇒x=-\frac{164}{3}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{Verify}\mathrm{if}\mathrm{LHS}=\mathrm{RHS}.\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{Consider}\mathrm{LHS}=\frac{\mathrm{x}}{5}+11\phantom{\rule{0ex}{0ex}}=\frac{-\frac{164}{3}}{5}+11\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}=\frac{-164}{15}+11\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}=\frac{-164+165}{15}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}=\frac{1}{15}=\mathrm{RHS}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{Hence},\mathrm{verified}\mathrm{LHS}=\mathrm{RHS}.$

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