How do I solve the inequality 3q + 11 < 8q + 99?

To solve the inequality 3q + 11 < 8q + 99, we need to isolate the variable q. Here are the steps:

1. First, let’s subtract 3q from both sides to start isolating q:
2. 3q + 11 – 3q < 8q + 99 - 3q
3. This simplifies to:
4. 11 < 5q + 99

Next, we’ll subtract 99 from both sides:

1. 11 – 99 < 5q + 99 - 99
2. Which gives us:
3. -88 < 5q

Now, we divide both sides by 5 to solve for q:

1. -88 / 5 < q
2. This gives:
3. q > -rac{88}{5}

So, the solution to the inequality is q > -17.6.

To summarize, we first simplified the inequality by moving 3q to the right and 99 to the left, which allowed us to isolate q. Always remember to perform the same operation on both sides of the inequality sign!