Question

Plz solve this question.
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Answer 1

Step-by-step explanation:

Given :-

[(1-x)/3] -(3/2)[2-(x-5)/2] +[(x+3)/4] = 1

To find:-

Find the value of x ?

Solution :-

Given equation is

[(1-x)/3] -(3/2)[2-(x-5)/2] +[(x+3)/4] = 1

=> [(1-x)/3] -(3/2)[(4-(x-5))/2] +[(x+3)/4] = 1

=> [(1-x)/3] -(3/2)[(4-x+5)/2] +[(x+3)/4] = 1

=> [(1-x)/3] -(3/2)[(9-x)/2] +[(x+3)/4] = 1

=> [(1-x)/3] -[3(9-x)/(2×2)] +[(x+3)/4] = 1

=> [(1-x)/3] -[(27-3x)/4] +[(x+3)/4] = 1

LCM of 3 , 4 , 4 = 12

=> [ 4(1-x)-3(27-3x)+3(x+3) ] / 12 = 1

=> (4-4x-81+9x+3x+9)/12 = 1

=> [(9x+3x-4x)+(4-81+9)] /12 = 1

=> [ (12x-4x)+(13-81) ] /12 = 1

=> (8x-68)/12 = 1

=> 8x-68 = 1×12

=> 8x -68 = 12

=> 8x = 12+68

=> 8x = 80

=> x = 80/8

=> x = 10

Therefore, x = 10

Answer:-

The value of x for the given problem is 10

Check:-

If x = 10 then LHS of the given equation becomes

[(1-x)/3] -(3/2)[2-(x-5)/2] +[(x+3)/4]

=> [(1-10)/3] -(3/2)[2-(10-5)/2] +[(10+3)/4]

=> [ (-9/3) - (3/2) [2-(5/2)] + (13/4)]

=> (-3)-(3/2)[(4-5)/2] +(13/4)

=> -3-(3/2)(-1/2)+(13/4)

=> -3-(-3/4)+(13/4)

=> -3+(3/4)+(13/4)

=> (-12+3+13)/4

=> (-12+16)/4

=> 4/4

=>1

=>RHS

LHS = RHS is true for x = 10

Verified the given relations in the given problem.