Question

solve and verify :
x/2-5=x/3+1/2​

Answer 1

Value of x is 27.

Step-By-Step-Explanation

Given :-

x/2 - 5 = x/3 + 1/2

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To Find :-

We have to find the value of x.

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Solution :-

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

To Solve this we have to take the LCM, Both sides.

$\frac{x - 10}{2} = \frac{2x + 3}{6}$

Now, By cross multiplication method.

$6(x - 10) = 2(2x + 3) \\ \\ 6x - 60 = 4x - 6 \\ \\ 6x - 4x = - 6 + 60 \\ \\ 2x = 54 \\ \\ x = \frac{54}{2} \\ \\ x = 27$

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Verification :-

For, verification pit value of x both side and then put them equal if L.H.S is equal to R.H.S

Then, it will be verified

$\frac{27}{2} - \frac{5}{1} = \frac{27}{3} - \frac{1}{2} \\ \\ \frac{27 - 10}{2} = \frac{54 - 3}{6} \\ \\ \frac{17}{2} = \frac{51}{6} \\ \\ 8.5 = 8.5$

Therefore, L.H.S = R.H.S

Hence Veified