Question

please send the soln please pleSe please​

Answer 1

Given :

$\sf \bullet \:\: \dfrac{\dfrac{2}{3}x + 1}{x + \dfrac{1}{4}} \: = \: \dfrac{5}{3}$

To find : x

Identity used :

$\sf \bullet \:\: \dfrac{ \: \: 1 \: \: }{\dfrac{a}{b}} = \dfrac{b}{a}$

Solution :

$\sf \bullet \:\: \dfrac{\dfrac{2}{3}x + 1}{x + \dfrac{1}{4}} \: = \: \dfrac{5}{3} \\ \\ \sf \: take \: lcm \\ \sf \implies \:\: \dfrac{\dfrac{(2x \times 1) + (3 \times 1)}{3} }{ \dfrac{(4\times x) + (1 \times 1)}{4}} \: = \: \dfrac{5}{3} \\ \\ \sf \implies \:\: \dfrac{\dfrac{(2x + 3)}{3} }{ \dfrac{(4x + 1)}{4}} \: = \: \dfrac{5}{3} \\ \\ \sf \implies \:\: \dfrac{(2x + 3)}{3} \: \times \dfrac{4}{(4x + 1)} = \dfrac{5}{3} \\ \\ \sf \implies \:\: \: \dfrac{4 \times 2x \: + \:4 \times 3 }{3 \times 4x \: + 3 \times 1} = \dfrac{5}{3} \: \\ \\ \sf \implies \:\: \: \dfrac{8x + 12}{12x + 3} = \dfrac{5}{3} \\ \\ \sf \implies \:\:3 \times (8x + 12) = 5 \times (12x + 3) \\ \\ \sf \implies \:\:24x + 36 = 60x + 15 \\ \\ \sf \implies \:\:60x - 24x = 36 - 15 \\ \\ \sf \implies \:\:36x = 21 \\ \\ \sf \implies \:\:x = \dfrac{21}{36} \\ \\ \sf \implies \:\:x \: = \bold{ \dfrac{7}{12} }$

ANSWER :

x = 7/12