Question

the solution of the equation 3/4 ( n-1) = n-3 is

Answer 1

Hello

3/4(n-1) = n- 3

3(n-1)/4 = n - 3

3n - 3/4 = n-3

3n-3 = 4(n-3)

3n - 3 = 4n -12

4n - 3n = 12- 3

n = 9

in your 2nd question

Gagan is thinking of a number .when he divided by 3 and then adds 4, the answer is half of the number .find the number

Let the number be x

given in the question

x divided by 3 +4 = half the number

x/3+4 = x/2

now,

x + 4*3/3 = x/2 (we took common in the denominator)

x+12/3= x/2

x+12 = 3*x/2 (we sent the 3 in the denominator to the numerator of the other side)

x+12 = 3x /2

(x +12)*2 = 3x (we sent the 2 in the denominator to the other side)

2x +24 = 3x

24 = 3x-2x

24= x

x= 24

Answer 2

$\huge \red { \boxed{ \boxed{ \mathsf{ \mid \ulcorner Answer :-\urcorner \mid }}}}$

Given :-

$\bf{ \frac{3(n - 1)}{4} = n - 3}$

Let this be equation 1.

To Find :-

Value of n.

Solution :-

$\sf{ \frac{3(n - 1)}{4} = n - 3 } \\ \\ \sf \implies{ \frac{3n - 3}{4} = n - 3 }$

By cross multiplication

$\sf \implies{3n - 3 = 4(n - 3)} \\ \\ \sf \implies{3n - 3 = 4n - 12} \\ \\ \sf \implies{3n - 4n = - 12 + 3} \\ \\ \sf \implies{ - n = - 9} \\ \\ \sf \implies{ \cancel- n = \cancel - 9}$

$\huge{\boxed{\blue{\sf{n = 9}}}}$

$\rule{200}{2}$

Verification :-

Put value of n in equation 1.

$\sf{\frac{3(9-1)}{4} = 9 - 3}$

$\implies{\sf{\frac{\cancel24}{\cancel4} = 6}}$

$\sf{\implies{6 = 6}}$

L. H. S = R. H. S

Hence, verified