Question

solve x from the following expression : x+2/3-x-3/4=x+1/5-1​

Answer 1

Answer:

Using Power Rules and Simple maths

4x−3x−12=3x+12−22x−1

22x+22x−1=3x+12+3x−12

22x+22x2=3x3–√+3x3√

22x(1+12)=3x(3–√+13√)

22x(32)=3x(43√)

22x(33–√)=3x(8)

22x332=3x23

Comparing Power of 2 2x=3, Comparing Power of 3 x=32

Both Equations give us

x=32

Answer 2

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

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

Now ,taking LCM of 3 & 4

LCM of 3 & 4 is 12

$\sf \longmapsto \dfrac{4(x + 2) - 3(x - 3)}{12} = \dfrac{x + 1}{4}$

$\sf \longmapsto \dfrac{4x + 8 - 3x + 9}{12} = \dfrac{x + 1}{4}$

$\sf \longmapsto \dfrac{x + 17}{12} = \dfrac{x + 1}{4}$

Now,cross multiply to both sides:

$\sf \longmapsto4(x + 17) = 12(x + 1)$

$\sf \longmapsto4x + 68 = 12x + 12$

$\sf \longmapsto68 - 12 = 12x - 4x$

$\sf \longmapsto56 = 8x$

$\sf \longmapsto \: x = \dfrac{56}{8} = 7$

$\sf\boxed{ \bold{x = 7}}$

Check:

$\sf \longmapsto4(x + 17) = 12(x + 1)$

Taking LHS

$\sf \longmapsto4(7 + 17)$

$\sf \longmapsto4(24) = 96$

Now taking RHS

$\sf \longmapsto12(x + 1)$

$\sf \longmapsto12(7 + 1)$

$\sf \longmapsto12(8)$

$\sf = 96$

Hence,LHS = RHS (Verified)