Question

Solve:2x-3/2+3x-2\3=2

Answer 1

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION\: \: } \mid}}}}}$

$\: \: \: \tt{2x - \frac{3}{2} + 3x - \frac{2}{3} = 2 } \\ \\ \tt{\Longrightarrow \: \frac{4x - 3}{2} + \frac{9x - 2}{3} = 2} \\ \\ \tt{\Longrightarrow \: \frac{3(4x - 3) + 2(9x - 2)}{6} = 2} \\ \\ \tt{\Longrightarrow \: \frac{12x - 9 + 18x - 4}{6} = 2 } \\ \\ \tt{\Longrightarrow \: \frac{30x - 13}{6} = 2 } \\ \\ \tt{\Longrightarrow \: 30x - 13 = 12} \\ \\ \tt{\Longrightarrow \:30x = 12 + 13 } \\ \\ \tt{\Longrightarrow \: 30x = 25} \\ \\ \tt{\Longrightarrow \: x = \frac{25}{30} } \\ \\ \: \: \: \: \: \: \tt{ \therefore \: \: x = \frac{5}{6} }$

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: VERIFICATION \: \: } \mid}}}}}$

$\tt{L.H.S. =2x - \frac{3}{2} + 3x - \frac{2}{3} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{ = 2 \times (\frac{5}{6} )- \frac{3}{2} + 3 \times ( \frac{5}{6}) - \frac{2}{3} } \\ \\\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{ = \frac{5}{3} - \frac{3}{2} + \frac{5}{2} - \frac{2}{3} } \\ \\\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{ = \frac{(10 - 9)}{6} + \frac{(15 - 4)}{6} } \\ \\\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{ = \frac{1}{6} + \frac{11}{6} } \\ \\\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{ = \frac{12}{6} } \\ \\\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{ = 2 = R.H.S. } \: \\ \\ \therefore \: \: \underline{ \tt{ \: \: L.H.S. = R.H.S. \: \: }}</p><p>$

Answer 2

Question :-

$\large\bf\red{2x - \frac{3}{2} + \frac{2}{3} = 2}$

$\huge\underline\textsf{Explantion:- }$

$\bf\rightarrow\frac{4x - 3}{2} + \frac{9x - 2}{3} = 2 \\ \\\bf\rightarrow\frac{3(4x - 3) + 2(9x - 2)}{6} = 2 \\ \\ \bf\rightarrow\frac{12 \times - 9 + 18x - 4}{6} = 2$

$\bf\rightarrow\frac{30x - 13}{6} = 2 \\ \\ \bf\rightarrow30 x - 13 = 12 \\ \\\bf\rightarrow 30x = 13 = 12$

$\bf\rightarrow30x = 12 + 3 \\ \\\bf\rightarrow30x = 25 \\ \bf\rightarrow x = \frac{\cancel2\cancel5}{\cancel3\cancel0}$

$\large\bf \rightarrow\frac{5}{6}$

$\huge\underline\textsf{Verification:- }$

$\bf\rightarrow L.H.S = 2x - \frac{3}{2} + 3x - \frac{2}{3}$

$\sf \rightarrow2 \times ( \frac{5}{6} ) - \frac{3}{2} + 3 \times ( \frac{5}{6} ) - \frac{2}{3}$

$\sf \rightarrow\red{\frac{5}{3} - \frac {3}{2} + \frac{5}{2} - \frac{2}{3 } }$

$\sf\rightarrow(\frac{10 - 9}{6} ) + (\frac{15 - 4}{6} )$

$\sf \frac{1}{6} + \frac{11}{6 } \\ \\ \bf\rightarrow\frac{\cancel1\cancel2}{\cancel6}$

$\large\bf \rightarrow\green{2 = \: R.H.S}$

L. H. S = R. H. S