Question

please verify the answer ...............hint answer x = 18/37......................I want only verification process............ or you can also give find x for you satification ...​

Answer 1

Answer:

X/3-2/5/3/4-2x=16/15 ( cross multiplication)

5x-6/15/3-8x/4 =16/15

5x-15/15=16/15 ×3-8x/4 (decimals 15,15 canceled and also 4×4=16 so 4,16 canceled)

5x-6=4×3-8x (4÷3 and also 8)

5x-6= 12-32x

5x+32x=12+6

37x=18

X=18/37

Answer 2

Question:

Solve the given equation:

$\displaystyle{\sf\:\dfrac{\dfrac{x}{3}\:-\:\dfrac{2}{5}}{\dfrac{3}{4}\:-\:2x}\:=\:\dfrac{16}{15}}$

Answer:

The value of x is

$\displaystyle{\implies\boxed{\red{\sf\:x\:=\:\dfrac{18}{37}}}}$

Step-by-step-explanation:

The given equation is $\displaystyle\sf\:\dfrac{\dfrac{x}{3}\:-\:\dfrac{2}{5}}{\dfrac{3}{4}\:-\:2x}\:=\:\dfrac{16}{15}$.

Now,

$\displaystyle{\sf\:\dfrac{\dfrac{x}{3}\:-\:\dfrac{2}{5}}{\dfrac{3}{4}\:-\:2x}\:=\:\dfrac{16}{15}}$

$\displaystyle{\implies\sf\:\dfrac{\dfrac{5x\:-\:6}{15}}{\dfrac{3\:-\:8x}{4}}\:=\:\dfrac{16}{15}}$

$\displaystyle{\implies\sf\:\dfrac{5x\:-\:6}{15}\:\times\:\dfrac{4}{3\:-\:8x}\:=\:\dfrac{16}{15}}$

$\displaystyle{\implies\sf\:\dfrac{4\:\times\:(\:5x\:-\:6\:)}{15\:\times\:(\:3\:-\:8x\:)}\:=\:\dfrac{16}{15}}$

$\displaystyle{\implies\sf\:\dfrac{20x\:-\:24}{45\:-\:120x}\:=\:\dfrac{16}{15}}$

$\displaystyle{\implies\sf\:15\:\times\:(\:20x\:-\:24\:)\:=\:16\:\times\:(\:45\:-\:120x\:)}$

$\displaystyle{\implies\sf\:300x\:-\:360\:=\:720\:-\:1920x}$

$\displaystyle{\implies\sf\:300x\:+\:1920x\:=\:720\:+\:360}$

$\displaystyle{\implies\sf\:2220x\:=\:1080}$

$\displaystyle{\implies\sf\:x\:=\:{\dfrac{108\cancel{0}}{222\cancel{0}}}}$

$\displaystyle{\implies\sf\:x\:=\:\cancel{\dfrac{108}{222}}}$

$\displaystyle{\implies\boxed{\red{\sf\:x\:=\:\dfrac{18}{37}}}}$

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Verification:

The given equation is

$\displaystyle{\sf\:\dfrac{\dfrac{x}{3}\:-\:\dfrac{2}{5}}{\dfrac{3}{4}\:-\:2x}\:=\:\dfrac{16}{15}}$

The value of x is $\displaystyle\sf\:\dfrac{18}{37}$

By substituting this value of x in the LHS of the given equation, we get,

$\displaystyle\sf\:LHS\:=\:\dfrac{\dfrac{x}{3}\:-\:\dfrac{2}{5}}{\dfrac{3}{4}\:-\:2x}$

$\displaystyle{\implies\sf\:LHS\:=\:\dfrac{\dfrac{\dfrac{18}{37}}{3}\:-\:\dfrac{2}{5}}{\dfrac{3}{4}\:-\:2\:\times\:\dfrac{18}{37}}}$

$\displaystyle{\implies\sf\:LHS\:=\:\dfrac{\dfrac{\cancel{18}}{37}\:\times\:\dfrac{1}{\cancel{3}}\:-\:\dfrac{2}{5}}{\dfrac{3}{4}\:-\:\dfrac{39}{37}}}$

$\displaystyle{\implies\sf\:LHS\:=\:\dfrac{\dfrac{6}{37}\:-\:\dfrac{2}{5}}{\dfrac{3}{4}\:-\:\dfrac{36}{37}}}$

$\displaystyle{\implies\sf\:LHS\:=\:\dfrac{\dfrac{6\:\times\:5\:-\:2\:\times\:37}{37\:\times\:5}}{\dfrac{3\:\times\:37\:-\:36\:\times\:4}{4\:\times\:37}}}$

$\displaystyle{\implies\sf\:LHS\:=\:\dfrac{\dfrac{30\:-\:74}{185}}{\dfrac{111\:-\:144}{148}}}$

$\displaystyle{\implies\sf\:LHS\:=\:\dfrac{\dfrac{-\:44}{185}}{\dfrac{-\:33}{148}}}$

$\displaystyle{\implies\sf\:LHS\:=\:\dfrac{\cancel{-}\:44}{185}\:\times\:\dfrac{148}{\cancel{-}\:33}}$

$\displaystyle{\implies\sf\:LHS\:=\:\cancel{\dfrac{\cancel{44}}{185}}\:\times\:\dfrac{148}{\cancel{33}}}$

$\displaystyle{\implies\sf\:LHS\:=\:\dfrac{4}{185}\:\times\:\dfrac{148}{3}}$

$\displaystyle{\implies\sf\:LHS\:=\:\dfrac{4\:\times\:148}{185\:\times\:3}}$

$\displaystyle{\implies\sf\:LHS\:=\:\cancel{\dfrac{592}{555}}}$

$\displaystyle{\implies\sf\:LHS\:=\:\dfrac{16}{15}}$

$\displaystyle{\implies\sf\:RHS\:=\:\dfrac{16}{15}}$

$\displaystyle{\implies\boxed{\red{\sf\:LHS\:=\:RHS}}}$

Hence verified!