Question

If the replacement set is the set of whole numbers, solve: $7-3x\ge \frac{-1}{2}$.

• A. {2, 3, 4, 5}
• B. {6, 7, 8}
• C. {9, 10, 11}
• D. {0, 1, 2}

Answer 1

The correct option is D {0, 1, 2}

Given: $7-3x\ge \frac{-1}{2}$

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 above inequation.

$\Rightarrow -3x\ge \frac{-1}{2}-7$

$\Rightarrow -3x\ge \frac{-15}{2}$

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 inequation by -1, we get

$\Rightarrow 3x\le \frac{15}{2}$

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 3 in both the inequations;

$\Rightarrow x\le \frac{15}{2}\times \frac{1}{3}$

$\Rightarrow x\le \frac{15}{6}$

$\Rightarrow x\le \frac{5}{2}$

$\Rightarrow x\le 2.5$
$\therefore$ The solution set is {0, 1, 2}.