If 5x-3 - 8 - 3x - 4 - 9x-2 - 2- find x-

The correct option is A 15 Simplifying both sides of #160; ( 5x+3 ) #160;/ 8 + 3x / 4 = 9x+2 / 2 #160; #160;separately, we get,LHS ...

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Standard XII

Mathematics

Sum of Coefficients of All Terms

If 5x+3 / ...

Question

If $\frac{(5 x + 3)}{8} + \frac{3 x}{4} = \frac{9 x + 2}{2}$ , find $x$ .

- \frac{1}{5}

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- 5

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\frac{1}{5}

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Solution

The correct option is A $- \frac{1}{5}$
Simplifying both sides of $\frac{(5 x + 3)}{8} + \frac{3 x}{4} = \frac{9 x + 2}{2}$ separately, we get,

LHS $= \frac{(5 x + 3)}{8} + \frac{3 x}{4} \times \frac{2}{2} = \frac{(5 x + 3)}{8} + \frac{6 x}{8}$ ....[Taking LCM]

$= \frac{5 x + 3 + 6 x}{8} = \frac{11 x + 3}{8}$ .

RHS $= \frac{9 x + 2}{2}$

$= \frac{9 x + 2}{2} \times \frac{4}{4} = \frac{36 x + 8}{8}$ .

Now, equating LHS and RHS, we get,
$⟹ \frac{11 x + 3}{8} = \frac{36 x + 8}{8}$ .

Multiplying both sides by $8$ ,
$⟹ 11 x + 3 = 36 x + 8$ .

Transposing $x$ terms to one side, we get,
$⟹ 36 x - 11 x = 3 - 8$

$⟹ 25 x = - 5$

$⟹ x = - \frac{5}{25}$

$⟹ x = - \frac{1}{5}$ .

Hence, option $A$ is correct.

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