Question

If the replacement set is the set of natural numbers (N), then find the solution set for the given inequation $1+9x\ge x+81$.

• A. $\{x:x\ge 10,x\epsilon W)$
• B. $\{x:x\ge 11,x\epsilon R)$
• C. $\{x:x\le 10,x\epsilon W)$
• D. $\{x:x>10,x\epsilon W)$

Answer 1

The correct option is A $\{x:x\ge 10,x\epsilon W)$

Given: $1+9x\ge x+81$
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.

$\Rightarrow 9x-x\ge 81-1$

$\Rightarrow 8x\ge 80$

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 8 in the inequation;

$\Rightarrow x\ge \frac{80}{8}$

$\Rightarrow x\ge 10$
Since, the replacement set is a set of whole numbers, therefore $\{x:x\ge 10,x\epsilon W\}$