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}

The given inequation is
$7-3x\ge \frac{-1}{2}$
$-3x\ge \frac{-1}{2}-7-3x\ge \frac{-15}{2}$
On multiplying the above inequation with -1, we get,
$3x\le \frac{15}{2}$ $\because \text{If we multiply a given inequation by a negative number, the sign of the inequality reverses}$
$\Rightarrow$$x\le \frac{15}{2}\times \frac{1}{3}x\le \frac{15}{6}x\le \frac{5}{2}x\le 2.5$
$\therefore$ The solution set is {0,1,2}