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The equation |2ax-3|+|ax+1|+|5-ax|=(1)/(...

The equation `|2ax-3|+|ax+1|+|5-ax|=(1)/(2)` possesses

A

Infinite number of real solutions for some `a in R`

B

finitely many real solutions for some `a in R''`

C

no real solutions for some `a in R`

D

no real solutions `a in R`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` We have `|2ax-3|+|ax+1|+|5-ax|=(1)/(2)`
Now
`|2ax-3|+|ax+1|+|5-ax| ge |2ax-3-(ax+1)+5-ax|=1`
So the given equation has no solution.
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