Question

Which of the following is the solution of the inequation
$27\le 3x\le 48$? ($x$ is a natural number)

• A. {9, 10, 11, 12, 13, 14, 15, 16}
• B. {-9, -10, -11, -12, -13, -14, -15, -16}
• C. {10, 11, 12, 13, 14, 15}
• D. {9, 10, 11, 12, 13}

Answer 1

The correct option is A {9, 10, 11, 12, 13, 14, 15, 16}

Given: $27\le 3x\le 48$

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 the inequation;

$\Rightarrow \frac{27}{3}\le \frac{3x}{3}\le \frac{48}{3}$

$\Rightarrow 9\le x\le 16$
$\therefore x=\text{9, 10, 11, 12, 13, 14, 15, 16}$.