Question

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Answer 1

Step by step explanation :-

Given :-

$\dfrac{x - 3}{2} - \dfrac{x - 1}{5} = \dfrac{2x - 3}{5}$

Solution :-

LCM of 2, 5 IS 10 in LHS

$\dfrac{(x - 3) 5 - (x - 1) 2}{10} = \dfrac{2x - 3}{5}$

$\dfrac{5x - 15 - (2x - 2)}{10} = \dfrac{2x - 3}{5}$

$\dfrac{5x - 15 - 2x + 2}{10} = \dfrac{2x - 3}{5}$

$\dfrac{3x - 13}{10} = \dfrac{2x - 3}{5}$

$\dfrac{3x - 13}{2} = 2x - 3$

Do Cross multiplication

$3x - 13 = 2(2x - 3)$

$3x - 13 = 4x - 6$

$3x - 4x = 13 - 6$

$- x = 7$

$x = \: - 7$

So, the value of x is -7

Verification :-

Substitute value of x It should be equal to LHS = RHS

$\dfrac{x - 3}{2} - \dfrac{x - 1}{5} = \dfrac{2x - 3}{5}$

x = -7

$\dfrac{-7 -3}{2} - \dfrac{-7 - 1 }{5} = \dfrac{2(-7) -3}{5}$

$\dfrac{-10}{2} - \dfrac{-8 }{5} = \dfrac{-14 -3 }{5}$

$\dfrac{-5}{1} - \dfrac{-8}{5} = \dfrac{-17}{5}$

$\dfrac{-5}{1} + \dfrac{8}{5} = \dfrac{-17}{5}$

$\dfrac{-25 +8}{5} = \dfrac{-17}{5}$

$\dfrac{-17}{5} = \dfrac{-17}{5}$

LHS = RHS

Hence verified!

Answer 2

$\textbf{\large{\underline{\pink{ Question: }}}}$

$\dfrac{x - 3}{2} - \dfrac{x - 1}{5} = \dfrac{2x - 3}{5}$

$\textbf{\large{\underline{\orange{ Solution: }}}}$

$now \: we \: have \: to \: take \: lcm \: of \: 2 \: and \: 5 \\ lcm \: of \: 2 \: and \: 5 \: is \: 10$

$\dfrac{5x - 15 - (2x - 2)}{10}$

$\dfrac{5x - 15 - 2x + 2}{10} = \dfrac{2x - 3}{5}$

$\dfrac{3x - 13}{10} = \dfrac{2x - 3}{5}$

$\dfrac{3x - 13}{10} \times 5 = 2x - 3$

$\dfrac{3x - 13}{2} = 2x - 3$

$3x - 13 = 2(2x - 3)$

$3x - 13 = 4x - 6$

$3x - 4x = 13 - 6$

$-x = 7$

$\textbf{\large{\underline{\blue{ Answer: }}}}$

x=-7