3x + 55 5x 76 = x 23 6 ( 3x + 5 ) 5 ( 5x 7 )5 × 6 = x 23 ( 18x + 30 ) ( 25x 35 )30 = x 23 18x + 30 25x + 3530 = x 23 ...

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Byju's Answer

Standard X

Mathematics

Ratio

3x+5/5-5x-7/6...

Question

$\frac{3 x + 5}{5} - \frac{5 x - 7}{6} = \frac{x - 2}{3}$

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Solution

$\frac{3 x + 5}{5} - \frac{5 x - 7}{6} = \frac{x - 2}{3}$
$\frac{6 (3 x + 5) - 5 (5 x - 7)}{5 \times 6} = \frac{x - 2}{3}$
$\frac{(18 x + 30) - (25 x - 35)}{30} = \frac{x - 2}{3}$
$\frac{18 x + 30 - 25 x + 35}{30} = \frac{x - 2}{3}$
$\Rightarrow 3 (65 - 7 x) = 30 (x - 2)$
$\Rightarrow 195 - 21 x = 30 x - 60$
$\Rightarrow 30 x + 21 x = 195 + 60$
$\Rightarrow 51 x = 255$
$\Rightarrow x = \frac{255}{51} = 5$
Thus $x = 5$
Hence the correct answer is $5$ .

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Similar questions

Q. Solve:

\frac{3 x + 5}{5} - \frac{x - 2}{3} = \frac{5 x - 7}{6}

Q. Solve

\frac{x - 2}{3} + \frac{3 x - 5}{5} = \frac{5 x - 7}{6} - \frac{1}{10}

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x

and

y

\frac{y + 7}{5} = \frac{2 y - x}{4} + 3 x - 5

\frac{7 - 5 x}{2} + \frac{3 - 4 y}{6} = 5 y - 18

Solve :

$(i) \frac{1}{3} x - 6 = \frac{5}{2} (i i) \frac{2 x}{3} - \frac{3 x}{8} = \frac{7}{12} (i i i) (x + 2) (x + 3) + (x - 3) (x - 2) - 2 x (x + 1) = 0 (i v) \frac{1}{10} - \frac{7}{x} = 35 (v) 13 (x - 4) - 3 (x - 9) - 4 (x + 4) = 0 (v i) x + 7 - \frac{8 x}{3} = \frac{17 x}{6} - \frac{5 x}{8} (v i i) \frac{3 x - 2}{4} - \frac{2 x + 3}{3} = \frac{2}{3} - x (v i i i) \frac{x + 2}{6} - (\frac{11 - x}{3} - \frac{1}{4}) = \frac{3 x - 4}{12} (i x) \frac{2}{5 x} - \frac{5}{3 x} = \frac{1}{15} (x) \frac{x + 2}{3} - \frac{x + 1}{5} = \frac{x - 3}{4} - 1 (x i) \frac{3 x - 2}{3} + \frac{2 x + 3}{2} = x + \frac{7}{6} (x i i) x - \frac{x - 1}{2} = 1 - \frac{x - 2}{3} (x i i i) \frac{9 x + 7}{2} - (x - \frac{x - 2}{7}) = 36 (x i v) \frac{6 x + 1}{2} + 1 = \frac{7 x - 3}{3}$

Q. Solve

5 x - (4 x - 7) (3 x - 5) = 6 - 3 (4 x - 9) (x - 1)

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3x+55−5x−76=x−23

3x+55−5x−76=x−236(3x+5)−5(5x−7)5×6=x−23(18x+30)−(25x−35)30=x−2318x+30−25x+3530=x−23⇒3(65−7x)=30(x−2)⇒195−21x=30x−60⇒30x+21x=195+60⇒51x=255⇒x=25551=5Thus x=5Hence the correct answer is 5.

$\frac{3 x + 5}{5} - \frac{5 x - 7}{6} = \frac{x - 2}{3}$