Question

solve the inequality and graph the solution.
16 > 8a
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.
submit

Explanation:

Step1: Divide both sides by 8

To solve the inequality \(16 > 8a\), we divide both sides by 8. Since 8 is a positive number, the direction of the inequality sign remains the same. So we have \(\frac{16}{8} > \frac{8a}{8}\).

Step2: Simplify both sides

Simplifying \(\frac{16}{8}\) gives 2, and simplifying \(\frac{8a}{8}\) gives \(a\). So the inequality simplifies to \(2 > a\), or equivalently \(a < 2\).

To graph this solution on the number line:

• We have an open circle at 2 (because the inequality is \(a < 2\), not \(a \leq 2\), so the endpoint 2 is not included).
• Then we draw a ray to the left of 2 to represent all the numbers less than 2.

Answer:

The solution to the inequality \(16 > 8a\) is \(a < 2\). The graph has an open circle at 2 and a ray pointing to the left (towards negative infinity) from 2.