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Question

Find the smallest value of x for which  52x < 512 53x, where x is an integer.


  1. -1
  2. -1.5
  3. 0
  4. 1


Solution

The correct option is A -1

Given:    52x < 512 53x

 52x < 112 53x

Rule: If a term of an inequation is transferred from one side to the other side of the inequation, the sign of the term gets changed. Let's apply this rule in the above inequation.

 5112 < 2x 53x

 12 < 13x


Rule: If both the sides of an inequation are multiplied or divided by the same positive number, then the sign of the inequality will remain same.
On multiplying the above inequation by 3, we get;

 32<xx >1.5

Since replacement set is the set of integers, the smallest value of x is -1.

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