How do I solve the compound inequality 6b < 24 or 4b < 12 + 4?

To solve the compound inequality
6b < 24 or 4b < 12 + 4, we need to solve each part separately.

Step 1: Solve the first inequality

For the first part: 6b < 24.

To isolate b, divide both sides by 6:

6b < 24
b < 4

This means b can be any number less than 4.

Step 2: Solve the second inequality

Next, we handle the second part: 4b < 12 + 4.

First, simplify the right side:

4b < 12 + 4
4b < 16

Then, divide both sides by 4:

4b < 16
b < 4

Again, this means b can be any number less than 4.

Step 3: Combine the results

Since both inequalities lead to the same conclusion, we find that for the compound inequality 6b < 24 or 4b < 12 + 4, the solution remains:

b < 4

Thus, any value of b that is less than 4 will satisfy the compound inequality.