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Q.

From the option, the solution set of the inequality 1 2 +8x>5x− 3 2 ,x∈Z  is:


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a

x∈ −2 3 ,∞  

b

x∈ 2 3 ,∞  

c

x∈ −5 3 ,∞  

d

x∈ −2 3 ,5   

answer is A.

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Detailed Solution

Given, 1 2 +8x>5x− 3 2 ,x∈Z  .
Now, let us calculate the solution set of given inequality,
1 2 +8x>5x− 3 2 ⇒ 1 2 + 3 2 >5x−8x ⇒2>−3x ⇒ 2 3 >−x  
It can be rewritten as,
⇒− 2 3 <x ⇒x>− 2 3  
So, from above, x∈ −2 3 ,∞  .
The correct option is 1).
 
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