Question
$\frac{7}{\text{x}}+35=\frac{1}{10}$
✓
Answer
$\frac{7}{\text{x}}+35=\frac{1}{10}$
Subtracting $35$ from both sides, $\frac{7}{\text{x}}+35-35=\frac{1}{10}-35$
$\frac{7}{\text{x}}=\frac{1-350}{10}$
$\Rightarrow\frac{7}{\text{x}}=\frac{-349}{10}$
$\Rightarrow-349\times\text{x}=7\times10$
$\Rightarrow\text{x}=\frac{7\times10}{-349}=\frac{70}{-349}=\frac{-70}{349}$ (By cross multiplication)
$\therefore\text{x}=\frac{-70}{349}$
Verification: $\text{L.H.S}=\frac{7}{\text{x}}+35$
$=\frac{7}{\frac{-70}{349}}+35=\frac{-7\times349}{70}+35$
$=\frac{-349}{10}+35$
$=\frac{-349+350}{10}=\frac{1}{10}=\text{R.H.S}$
Subtracting $35$ from both sides, $\frac{7}{\text{x}}+35-35=\frac{1}{10}-35$
$\frac{7}{\text{x}}=\frac{1-350}{10}$
$\Rightarrow\frac{7}{\text{x}}=\frac{-349}{10}$
$\Rightarrow-349\times\text{x}=7\times10$
$\Rightarrow\text{x}=\frac{7\times10}{-349}=\frac{70}{-349}=\frac{-70}{349}$ (By cross multiplication)
$\therefore\text{x}=\frac{-70}{349}$
Verification: $\text{L.H.S}=\frac{7}{\text{x}}+35$
$=\frac{7}{\frac{-70}{349}}+35=\frac{-7\times349}{70}+35$
$=\frac{-349}{10}+35$
$=\frac{-349+350}{10}=\frac{1}{10}=\text{R.H.S}$
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