Question

if x+4/2+x-3/3=x+2/4+x+3/5 find the value of x​

Answer 1

Answer :

x=6/23

Explanation:

(x+4)/2+(x-3)/3=(x+2)/4+(x+3)/5

=> [3(x+4)+2(x-3)]/6=[(5(x+2)+4(x+3)]/20

=> [3x+12+2x-6]/6 = [5x+10+4x+12]/20

=> (5x+6)/6 = (9x+22)/20

Multiply both sides by 2 , we get

=> (5x+6)/3 = (9x+22)/10

=> 10(5x+6) = 3(9x+22)

=> 50x+60 = 27x+66

=> 50x-27x = 66 - 60

=> 23x = 6

=> x = 6/23

••••

Answer 2

$\bf\huge\textbf{\underline{\underline{According\:to\:the\:Question}}}$  

$\bf\huge{\implies\dfrac{x+4}{3} + \dfrac{x-3}{3} = \dfrac{x+2}{4} + \dfrac{x+3}{5}}$  

$\bf\huge{\implies\dfrac{3(x+4)+2(x-3)}{6} = \dfrac{5(x+2) +4(x+3)}{20}}$  

$\bf\huge{\implies\dfrac{3x+12+2x-6}{6} = \dfrac{5x+10+4x+12}{20}}$  

$\bf\huge{\implies\dfrac{5x+6}{6} = \dfrac{9x+22}{20}}$  

Multiply 2 with both sides of an equation

$\bf\huge{\implies\dfrac{5x+6}{3} = \dfrac{9x+22}{10}}$  

⇒ 10(5x + 6) = 3(9x + 22)

⇒ 50x + 60 = 27x + 66

⇒ 50x - 27x = 66 - 60

⇒ 23x = 6

$\bf\huge{\implies x =\dfrac{6}{23}}$