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Solve |3x-2|=x. and find the solution se...

Solve `|3x-2|=x`. and find the solution set

A

`{ 0 , 2/3} `

B

`{ 0 , 1}`

C

`{ 1/2 , 1} `

D

`{ 1 , 2}`

Text Solution

Verified by Experts

The correct Answer is:
C

|3x-2|=x
Case (i)
When `3x -2 ge 0 or x ge 2//3`
For which we have 2-3x= x or x=1
(ii) Case ,
When `3x-2 lt 0 or x lt 2//3`
For which we have `2-3x = x or x = 1//2`
Hence , solution set is { 1/2 , 1}
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