How do you solve the equation l2-3xl> 4 in the real number system? Its supposed to be the absolute value of 2 minus 3x greater than or equal to 4.
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jeew-m
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l2-3xl> 4
First we need to define l2-3xl . l2-3xl is always positive,
when l2-3xl > 0 then l2-3xl = 2-3x
Then 2-3x > 0 nad it gives 2/3 > x
when l2-3xl < 0 then l2-3xl = -(2-3x)
Then -(2-3x)>0 and it gives x > 2/3
So when x<2/3 then l2-3xl = 2-3x and when x>2/3 then l2-3xl = -(2-3x)
l2-3xl> 4
When `x<2/3`
`(2-3x)>4`
`2-4 > 3x`
`-2/3 > x`
When` x>2/3`
`-(2-3x)>4`
`3x > 4+2`
`x > 2`
So the answers for the inequality is;
`x<-2/3 and x>2 `
`x in (-oo,-2/3) U (2,oo) `
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