Find the least value of $x$ that satisfies the following inequation:
$- 27 + 2 x \leq 9$ ; $x ϵ N$

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Solution

Given: $- 27 + 2 x \leq 9$

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 given inequation.

$\Rightarrow 2 x \leq 9 + 27$

$\Rightarrow 2 x \leq 36$

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 the same.
On dividing both sides by 2 in both the inequations;

$\Rightarrow x \leq 18$

Since, $x ϵ N$ the least value $x$ can take is 1, while the highest value can be 18.

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