Question

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

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

Answer 1

The correct option is A

$\{x:x\ge 10,x\epsilon R)$

The given inequation is
$1+9x\ge x+81$
$\Rightarrow 9x-x\ge 81-1$ (when switching sides switch the signs)
$\Rightarrow 8x\ge 80$
$\Rightarrow x\ge \frac{80}{8}$
$\Rightarrow x\ge 10$ $(\because$ 8 is positive, the sign of inequality will not change)
$\{x:x\ge 10,x\epsilon R\}$