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Question

Solve for x : 3(81)x+3=9x+1+9x.


A

3 & 2

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B

±12

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C

4 & 5

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D

±1

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Solution

The correct option is B

±12


We have
3(81)x+3=9x+1+9x
3(92)x+3=9x9+9x
3(92)x+3=9x(9+1)
3(92)x+3=9x(10)
3(9x)2+3=9x(10)

Let 9x=t, then we have
3t210t+3=0
3t29tt+3=0
3t(t3)1(t3)=0
(3t1)(t3)=0
t=13,t=3
9x=13,3
32x=31,31
or 2x=1,2x=1
x=12,12


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