Solve it

The solution set of this inequality is the same as the set of those numbers on a number line, which are at most 2 units away from the number 3:

a = 3 - 2 = 1

b = 3 + 2 = 5

Hence, our answer should be:

$3ab = 3 × 1 × 5 = \boxed {15}$

For $x \ge 3$ the inequality becomes $x - 3 \le 2 \Longrightarrow x \le 5$ , so in this case the inequality holds on $[3,5]$ .

For $x \le 3$ the inequality becomes $3 - x \le 2 \Longrightarrow x \gt 1$ , so in this case the inequality holds on $[1,3]$ .

Combining these results we see that the inequality in general holds on $[1,5]$ , and so $3ab = 3 \times 1 \times 5 = \boxed{15}$ .