Question

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Answer 1

Question-

Solve-

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

Solution -

$\implies \: x - \frac{(x - 1)}{2} = 1 - \frac{x - 2}{3}$

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

$\implies \frac{2x - x + 1}{2} = \frac{3 - x + 2}{3}$

$\implies \frac{x + 1}{2} = \frac{5 - x}{3}$

By cross multiplying,

$\implies2(5 - x) = 3(x + 1)$

$\implies10 - 2x = 3x + 3$

$\implies - 2x - 3x = 3 - 10$

$\implies - 5x = - 7$

$\implies \: x = \frac{ - 7}{ - 5}$

$\boxed{{{x = \frac{7}{5}}}}$

Verification -

L. H. S

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

Putting the value of x = 7/5

$= \frac{7}{5} - \frac{ \frac{7}{5} - 1 }{2}$

$= \frac{7}{5} - \frac{ \frac{7 - 5}{5} }{2}$

$= \frac{7}{5} - \frac{ \frac{2}{5} }{2}$

$= \frac{7}{5} - \frac{2}{5 \times 2}$

$= \frac{7}{5} - \frac{2}{10}$

$= \frac{14 - 2}{10}$

$= \frac{12}{10}$

$= \frac{6}{5}$

R. H. S

$= 1 - \frac{x - 2}{3}$

Putting the value of x=7/5

$= 1 - \frac{ \frac{7}{5} - 2}{3}$

$= 1 - \frac{ \frac{ 7 - 10}{5} }{3}$

$= 1 - \frac{ \frac{ - 3}{5} }{3}$

$= 1 - \frac{ - 3}{3 \times 5}$

$= 1 - \frac{ - 3}{15}$

$= \frac{15 - ( - 3)}{15}$

$= \frac{15 + 3}{15}$

$= \frac{18}{15}$

$= \frac{6}{5}$

Therefore L. H. S=R. H. S

Hence verified