N.5 Graph solutions to one-step inequalities

Question

TMX
Solve the inequality and graph the solution.
2n≤8
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 \(2n \leq 8\), follow these steps:

Step 1: Solve the inequality. To isolate \(n\), divide both sides of the inequality by 2:

\[ n \leq \frac{8}{2} \]

\[ n \leq 4 \]

Step 2: Graph the solution. The solution \(n \leq 4\) means that \(n\) can take any value up to and including 4.

• Endpoint: Mark the point \(4\) on the number line.
• Type of endpoint: Since \(n\) can equal \(4\), you'll use a closed circle (or filled dot) at \(4\).
• Direction of ray: Draw a ray extending to the left from the point \(4\), indicating all values less than or equal to \(4\).

Visualization:

• Draw a horizontal line (the number line).
• Place a closed circle at \(4\).
• Draw an arrow extending left from \(4\) to indicate that the inequality includes all numbers less than \(4\).

This completes the graphing of the solution to the inequality \(2n \leq 8\). The graph visually represents that \(n\) can take values up to and including \(4\).