Question

find the linear equation of:
$\frac{3x}{4} - \frac{2x + 5}{3} = \frac{5}{2}$
​

Answer 1

$\bf\huge\underline{\underline{ Given :- }}$

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

$\bf\huge\underline{\underline{ To \: Find:- }}$

• value of x

$\bf\huge\underline{\underline{ Answer :- }}$

• $\red{\implies} \large\sf \frac{3x}{4} - \frac{2x + 5}{3} = \frac{5}{2}$

• $\red{\implies} \large\sf \: \frac{3x . 3 - (4 .2x + 5.4)}{4.3} = \frac{5}{2}$

• $\red{\implies} \large\sf \: \frac{9x - 8x - 20}{12} = \frac{5}{2}$

• $\red{\implies} \large\sf \frac{x - 20}{12} = \frac{5}{2}$

• $\red{\implies} \large\sf \: x - 20 = \frac{5 \times 12}{2}$

• $\red{\implies} \large\sf \: x - 20 = 5 \times 6$

• $\red{\implies \large\sf \: x - 20 = 30 }$

• $\red{\implies \large\sf \: x =30 + 20 }$

• $\red{\implies \large\sf \: \underline{x = 50} }$

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Answer 2

❐QuEsTiOn,

find the linear equation of:

$\sf \color{red} \hookrightarrow \: \frac{3x}{4} - \frac{2x + 5}{3} = \frac{5}{2}$

❐SoLuTiOn,

$\sf \color{blue} \hookrightarrow \: \frac{3x}{4} - \frac{2x + 5}{3} = \frac{5}{2}$

$\sf \color{red} \hookrightarrow \: \frac{ 3(3x)- 4(2x + 5)}{12} = \frac{5}{2}$

$\sf \color{blue} \hookrightarrow \: \frac{9x- 8x - 20}{12} = \frac{5}{2}$

$\sf \color{red} \hookrightarrow \: \frac{x - 20}{12} = \frac{5}{2}$

$\sf \color{blue} \hookrightarrow \: 2(x - 20) = {12(5)}$

$\sf \color{red} \hookrightarrow \: 2x - 40 = 60$

$\sf \color{blue} \hookrightarrow \: 2x = 60 + 40$

$\sf \color{red} \hookrightarrow \: 2x =100$

$\sf \color{blue} \hookrightarrow \: x = \frac{100}{2}$

$\sf \color{red} \boxed{ \sf \hookrightarrow \: x = 50}$

❐VeRiFiCaTiOn,

$\sf \color{blue} \hookrightarrow\frac{3x}{4} - \frac{2x + 5}{3} = \frac{5}{2}$

$\sf \color{red} \hookrightarrow\frac{3(50)}{4} - \frac{2(50)+ 5}{3} = \frac{5}{2}$

$\sf \color{blue} \hookrightarrow\frac{150}{4} - \frac{100+ 5}{3} = \frac{5}{2}$

$\sf \color{red} \hookrightarrow\frac{75}{2} - \frac{105}{3} = \frac{5}{2}$

$\sf \color{blue} \hookrightarrow\frac{75}{2} - 35 = \frac{5}{2}$

$\sf \color{red} \hookrightarrow\frac{75 - 2(35)}{2} = \frac{5}{2}$

$\sf \color{blue} \hookrightarrow\frac{75 - 70}{2} = \frac{5}{2}$

$\sf \color{red} \hookrightarrow\frac{5}{2} = \frac{5}{2}$

$\sf \color{blue} \boxed{ \sf\hookrightarrow LHS = RHS}$

$\sf \color{red}\hookrightarrow \: Hence,Proved$

❐FiNal AnSwEr,

$\sf \color{red} \boxed{ \sf \hookrightarrow \: x = 50}$

❥Hope you get your AnSwEr.