Question

$solve \: the \: following \: equation \: and \: check \: \\ your \: solution \: \\ \frac{3x + 5}{2x+ 7} \: = 4$
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Answer 1

Step-by-step explanation:

$\frac{3x + 5}{2x + 7} = 4 \\ 3x + 5 = 4(2x + 7) \\ 3x + 5 = 8x + 28 \\ 8x - 3x = 5 - 28 \\ 5x = - 23 \\ x = \frac{ - 23}{5} \: \: \: ans$

Answer 2

GIVEN :-

$\\ \bigstar \displaystyle \sf \dfrac{(3x + 5)}{(2x + 7)} = 4$

TO FIND :-

$\\ \bigstar \displaystyle \sf \: The \: value \: of \: x.$

SOLUTION :-

$\\ \\ : \implies \displaystyle \sf \dfrac{(3x + 5)}{(2x + 7)} = 4$

$\dag\displaystyle \rm \: By \: cross \: multiplication.$

$: \implies \displaystyle \sf \: 4(2x + 7) = (3x + 5)$

$: \implies \displaystyle \sf \: 8x + 28 = 3x + 5$

$: \implies \displaystyle \sf \: 8x - 3x = 5 - 28$

$: \implies \displaystyle \sf \: 5x = - 23$

$: \implies \underline{ \boxed{ \displaystyle \sf \: x = \frac{ - 23}{5} }} \: \: \: \: \: \: \: \: \: \: \: \: \bigg \lgroup \displaystyle \sf \:Value \: of \: x \: \bigg \rgroup$

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VERIFICATION :-

$\\ : \implies \displaystyle \sf \dfrac{(3x + 5)}{(2x + 7)} = 4$

$\dag \: \displaystyle \rm \: put \: the \: value \: of \: x.$

$: \implies \displaystyle \sf \: \frac{3 \times \bigg( \dfrac{ - 23}{5} \bigg) + 5}{2 \times \bigg(\dfrac{ - 23}{5} \bigg) + 7 } = 4$

$: \implies \displaystyle \sf \: \frac{ \bigg( \dfrac{ - 69}{5} + 5 \bigg)}{ \bigg(\dfrac{ - 46}{5} + 7 \bigg)}$

$: \implies \displaystyle \sf \frac{ \bigg(\dfrac{ - 69 + 25}{5} \bigg)}{ \bigg( \dfrac{ - 46 + 35}{5} \bigg) }$

$: \implies \displaystyle \sf \: \frac{ - 44}{ - 11} = 4$

$: \implies \displaystyle \sf \: 4 = 4$

$\bigstar \ \underline {\boxed{\displaystyle \sf L.H.S = R.H.S}} \ \ \ \ \ \ \bigg \lgroup \displaystyle \sf Hence \ verified \ \bigg\rgroup$