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For a in R, if |x - a + 3| + |x-3a|=2x ...

For a `in` R, if `|x - a + 3| + |x-3a|=2x - 4a +3 |` is ture `AA x in`R. Then find the value of a.

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`|x - a + 3| + |x-3a|=2x - 4a +3|`
`rArr |x - a + 3| + |x-3a|=|(x - a +3) + (x - 3a)|`
`rArr (x - a + 3 )(x - 3a)ge0 AA x in`R.
`rArr x^(2) + x (3 - 4a) + 3a (a - 3) ge 0, AA x in n` R.
For the above inequality,
`D le 0`
`rArr (3 - 4 a)^(2) - 12 a (a - 3) le 0`
`rArr (2a + 3)^(2) le 0`
`rArr a = - 3//2`
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