Find the smallest value of x for which 5−2x < 512 −53x, where x is an integer.
Given: 5−2x < 512 −53x
⇒ 5−2x < 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.
⇒ 5−112 < 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<x→x >−1.5
Since replacement set is the set of integers, the smallest value of x is -1.