Question

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Answer 1

$\huge \underline{ \boxed{ \bf \red{ANSWER}}}$

$\sf \frac{x + 1}{2} + 2x + 1 = \frac{2x + 4}{2} + (1 - 2x) + 2$

$\frac{x + 1 + 4x + 2}{2} = \frac{2x + 4}{2} + 1 - 2x + 2$

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

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

$\sf multiply \: both \: equations \: by \: 2 \brack$

$\frac{ \cancel2(5 x + 3 )}{ \cancel2} = \frac{ \cancel2(10 - 2x)}{ \cancel2}$

$5x + 3 = 10 - 2x$

$5x + 2x = 10 - 3$

$7x = 7$

$x = \cancel\frac{7}{7}$

$\large \underline{ \boxed { \blue{x=1}}}$

$\sf \underline{ \purple{Important \: property \: included \: is \: LCM.}}$

Answer 2

$\pink{QuestioN:}$

$\red{If\: \frac{x+1}{2}+2x+1=\frac{2x+4}{2}+(1-2x)+2,\:find\:x? }$

$\huge\mathcal{\fcolorbox{cyan}{black}{\pink{Answer:}}}$

$\green{\frac{x+1}{2}+2x+1=\frac{2x+4}{2}+(1-2x)+2,}$

$\pink{\frac{x+1+2x+1}{2} =\frac{2x+4+2(1-2x)+4}{2} }$

$\pink{\frac{5x-3}{2}=\frac{10-2x}{2} }$

$\green{Multiply\:by\:2\:on\:both\:sides}$

$\red{\frac{2(5x-3)}{2}=\frac{2(10-2x)}{2}}$

$\gold{\frac{(10x-6)}{2}=\frac{(20-4x)}{2} }$

$\pink{2(10x-6)=2(20-4x)}\\\\\red{20x-12=40-6x}\\\\\pink{26x=52}\\\\\red{x=2.}$

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