Question

solve the inequality and graph the solution.\\(9 + 2a < 1\\)\
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.

Explanation:

Step1: Subtract 9 from both sides

To isolate the term with \(a\), we subtract 9 from both sides of the inequality \(9 + 2a < 1\). This gives us \(9 + 2a - 9 < 1 - 9\), which simplifies to \(2a < -8\).

Step2: Divide both sides by 2

To solve for \(a\), we divide both sides of the inequality \(2a < -8\) by 2. This results in \(\frac{2a}{2} < \frac{-8}{2}\), so \(a < -4\).

To graph the solution:

• The endpoint is at \(a = -4\). Since the inequality is strict (\(<\), not \(\leq\)), we use an open circle at \(-4\).
• Then, we draw a ray to the left of \(-4\) to represent all values of \(a\) less than \(-4\).

Answer:

The solution to the inequality is \(a < -4\). For the graph, place an open circle at \(-4\) on the number line and draw a ray pointing to the left (towards more negative numbers) from \(-4\).