Question

solve x/2-1/5=x/3+1/4​

Answer 1

$\sf\huge {\underline{\underline{{Solution}}}}$

$\sf\implies \dfrac{x}{2} - \dfrac{1}{5} = \dfrac{x}{3} + \dfrac{1}{4}$

Now, firstly taking LCM on both sides

LCM of 2 and 5 is 10

LCM of 3 and 4 is 12

$\sf\implies \dfrac{5x - 2}{10} = \dfrac{4x + 3}{12}$

Now,cross multiply to both sides:

$\sf\implies12(5x - 2) = 10(4x + 3)$

Expanding the terms and opening the brackets:

$\sf\implies60x - 24 = 40x + 30$

Now,shifts Variable to Variable side and constant term together

$\sf\implies60x - 40x = 30 + 24$

$\sf\implies20x = 54$

$\sf\implies \: x = \dfrac{54}{20} = \dfrac{27}{10} = \bold{2.7}$

$\sf\large\therefore \: x \: is \: \red{2.7}$

Check:

$\sf\implies20x = 54$

$\sf\implies \: 20 \times 2.7 = 54.0 = 54$

Answer 2

Answer:

      x = 2.7

Step-by-step explanation:

G.T.,

    $\frac{x}{2} - \frac{1}{5} = \frac{x}{3} + \frac{1}{4}$

    $\frac{5x - 2}{10} = \frac{4x + 3}{12}$

    $12 (5x - 2) = 10 (4x + 3)$

    $60x - 24 = 40x + 30$

    $60x - 40x = 30 + 24$

    $20x = 54$

    $x = \frac{54}{20}$

    $x = \frac{27}{10} (or) 2.7$

∵ Hence, we got the answer x = 2.7