How do you determine the solution set for the inequality 3x ≤ 12 and 100 ≥ 0?

Understanding the Inequalities

The given problem presents a system of inequalities that we need to solve. The inequalities are:

• 3x ≤ 12
• 100 ≥ 0

Breaking Down Each Inequality

Let’s tackle each inequality one at a time:

1. Solving 3x ≤ 12

To isolate x, we need to divide both sides of the inequality by 3:

3x ≤ 12
x ≤ 12 / 3
x ≤ 4

This tells us that x can take any value up to and including 4. In interval notation, we can express this as:

(-∞, 4]

2. Evaluating 100 ≥ 0

This is a constant inequality, and since 100 is always greater than 0, it doesn’t impose any restrictions on the solution set for x. Essentially, it holds true for all x.

Combining Our Results

The solution set is determined by the most restrictive condition, which in this case, is from the inequality 3x ≤ 12. Therefore, our overall solution set for the system is:

(-∞, 4]

Final Solution

Thus, the solution set for the inequalities 3x ≤ 12 and 100 ≥ 0 is:

(-∞, 4]