Question

x/2+3/2=2x/5-1 solve the following linear equations​

Answer 1

Answer:

x = -25

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Step-by-step explanation:

$\\ \large \bf \dfrac{x}{2} + \dfrac{3}{2} = \dfrac{2x}{5 } -1\\ \\ \implies \bf \: \frac{x}{2} - \frac{2x}{5} = - 1 - ( \frac{3}{2} )\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \dag (LCM \: \: of \: \: 5 \: \: and \: \: 2 \: \: is \: \: 10)\\ \\ \implies \bf \frac{5x - 4x }{10} = \frac{ (- 2 - 3)}{2} \\ \\ \implies \bf \frac{x}{10} = \frac{ - 5}{ \: 2} \\ \\ \bf \implies \: x = (\frac{ - 5}{ \: 2} ) \times 10 \\ \\ \bf \implies \: x = \frac{ - 50}{ \: 2} \\ \\ \bf \implies \: x = - 25 \\ \\ {\underline{ \boxed{ \sf\therefore \: the \: \: vaue \: \: of \: \: x \: \: = \: \: - 25 \: }}}$

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Now let's verify !

Substitute value of x = -25 in the given equation.

$\large \bf \dfrac{x}{2} + \dfrac{3}{2} = \dfrac{2x}{5 } - 1\\ \\ \bf \implies \dfrac{ - 25}{2} + \dfrac{3}{2} = \dfrac{2( - 25)}{5 } - 1 \\ \\ \bf \implies \dfrac{ - 25}{2} + \dfrac{3}{2} = \dfrac{ - 50}{5 } - 1\\ \\ \bf \implies \dfrac{ - 25 + 3}{2} = \dfrac{ - 50}{5} - 1 \\ \\ \bf \implies \frac{ - 22}{2} = \frac{ \cancel{ - 50} {}^{10} }{ \cancel{5} {}^{1} } \\ \\ \bf \implies - 11 = - 11 \\ \\ \: \: \: \: \: \: \: \: \: \boxed{\boxed{ \rm LHS = RHS }}\\ \\ \: \: \: \: \: \: \: \: \: \sf \: Hence, verified\\ \\ \sf \therefore \:The \: \: value \: \: of \: \: x \: = - 25$