Question

Q:-solve and verify the equation
$\frac{1}{2} - \frac{1}{3} (x - 1) + 2 = 0$​

Answer 1

$\green{\bold{\underline{ ✪ UPSC-ASPIRANT✪ }}}$

$\red{\bold{\underline{\underline{QUESTION:-}}}}$

Q:-solve and verify the equation

$\frac{1}{2} - \frac{1}{3} (x - 1) + 2 = 0$

$\huge\tt\underline\blue{Answer }$

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$⟹ \frac{1}{2} - \frac{1}{3} (x - 1) + 2 = 0</p><p>$

$⟹</p><p> \frac{3 - 2(x - 1) + 2}{6} = 0$

$⟹</p><p> \frac{1}{6} (x - 1) + 2 = 0$

$⟹</p><p>(x - 1) + 2 = 0$

$⟹</p><p>x - 1 = - 2$

$⟹</p><p>x = - 2 + 1$

$⟹</p><p>x = - 1$

CHECK:-

$⟹ \frac{1}{2} - \frac{1}{3} ( - 1 - 1) + 2</p><p>$

$⟹</p><p> \frac{3 - 2( - 2) + 2}{6} = 0$

$⟹</p><p> \frac{1}{6} ( - 2) + 2 = 0$

$⟹</p><p> \frac{0}{6} = 0$

$⟹</p><p>0 = 0$

THEREFORE,L.H.S=R.H.S

VERIFIED ✔️

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Answer 2

Answer:-

$\sf ✯ \: \frac{1}{2} - \frac{1}{3} (x - 1) + 2 = 0$

$\sf ➜ \: \frac{3 - 2(x - 1) + 2}{6} = 0$

$\sf ➜ \: \frac{1}{6} (x - 1) + 2 = 0$

$\sf ➜ \: (x - 1) + 2 = 0$

$\sf ➜ \: x - 1 = - 2$

$\sf ➜ \: x = - 2 + 1$

$\sf ➜ \: x = - 1$

$\boxed{\sf x = - 1}$

$\sf \red {Therefore, \: value \: of \: x \: in \: above \: equation \: is \: -1}$

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Verification:-

$\sf ➜ \: \frac{1}{2} - \frac{1}{3} ( - 1 - 1) + 2 = 0$

$\sf ➜ \: \frac{3 - 2( - 2) + 2}{6} = 0$

$\sf ➜ \: \frac{1}{6} ( - 2) + 2 = 0$

$\sf ➜ \: \frac{0}{6} = 0$

$\sf ➜ \: 0 = 0$

$\sf \red {Hence, \: Verified}$