Question

$\sf{ \red{Solve \: the \: following \: :}}$
$\sf{i) \: \frac{1}{9} - \frac{4}{8} + \frac{3}{6} }$
$\sf{ii) \: 12 - 4\times \frac{1}{3} }$
$\sf{ \red {Solve \: the \: following \: equation \: : }}$
$\sf{a) \: 3(x - 2) + 7 = 22}$
$\sf{b) \: - 2(x - 5) + 7 = 17}$
​

Answer 1

Wait for attachment bro

I HOPE YOU'LL FIND IT HELPFULL ❤️❤️

Answer 2

Step-by-step explanation:

$\large\underline{\bf{Solution \: \: 1}}$

$\large {\frac{1}{9} - \frac{4}{8} + \frac{3}{6} }$

Take LCM of the denominators.

$3 \: \: \: | \: 9 \: \: \: \: 8 \: \: \: \: 6 \\ 3 \: \: \: | \: 3 \: \: \: \: 8 \: \: \: 2 \\2 \: \: \: | \: \: 1 \: \: \: 8 \: \: \: 2 \\ 2\: \: \: | \: 1 \: \: \: 4 \: \: \: 1 \\ 2 \: \: |\: 1 \: \: \: 2 \: \: \: 1 \\ \: \: \: \: \: \: \: 1 \: \: \: 1 \: \: \: 1$

$3 \times 3 \times 2 \times 2 \times 2 = 72$

$\small\boxed{\sf{ \frac{1 \times 8}{9 \times 8} - \frac{4 \times 9}{8 \times 9} + \frac{3 \times 12}{6 \times 12} }}$

$\large\underline{\sf{ \frac{8}{72} - \frac{36}{72} + \frac{36}{72} }}$

$\large\boxed{\sf{ \implies \frac{8}{72} }}$

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$\large\underline{\bf{Solution \: \: \: \: 2}}$

$\large\underline{\sf{12 - 4 \times \frac{1}{3} }}$

$\large\underline{\sf{12 - \frac{4}{3} }}$

Can be written as:-

$\large \underline{\sf{ \frac{12}{1} - \frac{4}{3} }}$

Take LCM:-

$3 |\: \: \: 1 \: \: \: 3 \\ \: \: \: \: \: \: \: \: 1 \: \: \: 1$

Hence 3 is the LCM:-

$\large\underline{\sf{ \frac{12 \times 3}{1 \times 3} - \frac{4 \times 1}{3 \times 1} }}$

$\large\underline{\sf{ \frac{36}{3} - \frac{4}{3} }}$

$\large\boxed{\sf{ \implies \frac{32}{3} }}$

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$\large\underline{\bf{Solution \: \: \: \: 3}}$

$\large\underline{\sf{3(x - 2) + 7 = 22}}$

$\large\underline{\sf{3x - 6 + 7 = 22}}$

$\large\underline{\sf{3x + 1 = 22}}$

$\large\underline{\sf{3x = 22 - 1}}$

$\large\underline{\sf{3x = 21}}$

$\large\underline{\sf{x = \frac{21}{3} }}$

$\large\boxed{\sf{ \implies x = 7}}$

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$\large\underline{\bf{Solution \: \: \: 4}}$

$\large\underline{\sf{ - 2(x - 5) + 7 = 17}}$

$\large\underline{\sf{ - 2x + 10 + 7 = 17}}$

$\large\underline{\sf{ - 2x + 17 = 17}}$

$\large\underline{\sf{ - 2x = 17 - 17}}$

$\large\underline{\sf{ - 2x = 0}}$

$\large\underline{ \sf{x = \frac{0}{ - 2} }}$

$\large\boxed{\sf{x = - \frac{0}{2} }}$