Let's solve this problem step by step:
First, we have the inequality 5 * (6 * v + 3) <= 30 * v + 18
We need to distribute the 5 that is on the outside of the parentheses on the left side of the inequality. That is applying the distributive property which implies that:
5 * 6v + 5 * 3 <= 30v + 18
This simplifies to:
30v + 15 <= 30v + 18
If we look at both sides of the inequality, we can see that we have the same term 30v on both sides. This term cancels out in the next step, leaving us with:
15 <= 18
This inequality is always true, since 15 is always less than or equal to 18.
Consequently, we have that the inequality holds true for every possible real number v.
Therefore, we can conclude that all real numbers are solutions to the given inequality.