Question

solve the inequality and graph the solution.
1 ≤ m - 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.
(number line with ticks at 0,1,2,3,4,5,6,7)

Explanation:

Step1: Add 8 to both sides

To solve the inequality \(1 \leq m - 8\), we add 8 to both sides to isolate \(m\).
\(1 + 8 \leq m - 8 + 8\)

Step2: Simplify both sides

Simplifying the left side gives \(9\) and the right side simplifies to \(m\). So we have \(9 \leq m\) or \(m \geq 9\).

For graphing, we plot a closed endpoint at 9 (since the inequality is "greater than or equal to") and draw a ray to the right (towards positive infinity) to represent all values of \(m\) that are greater than or equal to 9. (Note: The given number line in the image only goes up to 7, but the correct graph should have the endpoint at 9. If we assume a corrected number line extending beyond 7, we place a closed dot at 9 and an arrow pointing right.)

Answer:

The solution to the inequality \(1 \leq m - 8\) is \(m \geq 9\). For the graph, plot a closed endpoint at 9 and draw a ray to the right.