Solve the following equation- 2x-135-x-311-x-95-1

Given, 2x 135 x 311=x 95+1 .Since, L.C.M. of denominators 5,11,5 and 1=55 2x 135× 55 x 311× 55=x 95× 55+11× 55 #160; ...

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Standard VIII

Mathematics

Solving Equations with Variables on Both Sides

Solve the fol...

Question

Solve the following equation:
$\frac{2 x - 13}{5} - \frac{x - 3}{11} = \frac{x - 9}{5} + 1$

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Solution

Given, $\frac{2 x - 13}{5} - \frac{x - 3}{11} = \frac{x - 9}{5} + 1$ .

Since, $L . C . M .$ of denominators $5, 11, 5$ and $1 = 55$
$⟹$ $\frac{2 x - 13}{5} \times 55 - \frac{x - 3}{11} \times 55 = \frac{x - 9}{5} \times 55 + \frac{1}{1} \times 55$

$⟹$ $11 (2 x - 13) - 5 (x - 3) = 11 (x - 9) + 55$

$⟹$ $22 x - 143 - 5 x + 15 = 71 x - 99 + 55$ ...[By Distribution Law]

$⟹$ $22 x - 5 x - 11 x = - 99 + 55 + 143 - 15$ ...[Transposing $x$ terms to one side]

$⟹$ $6 x = 198 - 114$ ...[On simplifying]

$⟹$ $6 x = 84$

$⟹$ $x = \frac{84}{6}$ ...[Dividing $6$ on both sides]

$⟹$ $x = 14$ .

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Solve the following equation:2x−135−x−311=x−95+1

Solve the following equation:
$\frac{2 x - 13}{5} - \frac{x - 3}{11} = \frac{x - 9}{5} + 1$