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The solution of the inequation 4^(-x+0.5...

The solution of the inequation `4^(-x+0.5)-7.2^(-x) < 4,x in R` is

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The correct Answer is:
` x in (-2 , oo )`
`4^(-x+0.5)- 7.2^(-x) lt 4 2^(-x) lt 4 `
Let `2^(-2x)=t`
`therefore tgt0`
Now (1) reduces to `2t^2-7t lt 4`
`or 2t^7t-4 lt 0`
`or ( 2t +1 ) (t-4)lt 0`
`or (-1)/(2) lt t lt 4`
`rArr 0 lt 2^(-x) lt 4 `
`rArr -2 lt x lt oo`
`rArr x in (-2,oo)`
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