Question

If the replacement set is the set of whole numbers, solve the following inequation.
$8-x\ge -\frac{1}{2}$.

• A. $\{0,1,2,3,4,5,6,7,8\}$
• B. $\{0,1,2,3,4,5,6,7\}$
• C. $\{1,2,3,4,5,6,7,8,9\}$
• D. $\{0,1,2,3\}$

Answer 1

The correct option is A $\{0,1,2,3,4,5,6,7,8\}$

Given: $8-x\ge -\frac{1}{2}$
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 following inequations.

$\Rightarrow -x\ge \frac{-1}{2}-8$

$\Rightarrow -x\ge \frac{-1-16}{2}$

$\Rightarrow -x\ge \frac{-17}{2}$

Rule: If both the sides of an inequation are multiplied or divided by the same negative number, then the sign of the inequality will get reversed.
On multiplying the above in equation with -1, we get

$\Rightarrow x\le \frac{17}{2}$

$\Rightarrow x\le 8.5$

Since replacement set is the set of all whole numbers, hence solution set is $\{0,1,2,3,4,5,6,7,8\}$.