N.5 Graph solutions to one-step inequalities

Question

TMX
Solve the inequality and graph the solution.
2p≤6
To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.

Answer 1

To solve the inequality \(2p \leq 6\), we first isolate \(p\) by dividing both sides of the inequality by 2:

\[ p \leq \frac{6}{2} \]

This simplifies to:

\[ p \leq 3 \]

Now we have the inequality \(p \leq 3\).

Graphing the Solution:

1. Plot the endpoint: Place a point at \(p = 3\).
2. Type of endpoint: Since the inequality is "less than or equal to" (\(\leq\)), we use a closed dot at \(3\) to indicate that \(3\) is included in the solution.
3. Direction of the ray: Since we are looking for values of \(p\) that are less than or equal to \(3\), draw a ray that extends to the left from the closed dot.

This is how the graph would look:

<---●========>
      3

• The closed dot at \(3\) shows that \(3\) is part of the solution.
• The arrow extending to the left indicates all values less than \(3\) are included in the solution.

The solution set in interval notation is \((-\infty, 3]\).