Question

solve the inequality and graph the solution.
1 ≤ (q - 1)/3
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: Solve the inequality

Multiply both sides of the inequality \(1\leq\frac{q - 1}{3}\) by \(3\):
\(1\times3\leq\frac{q - 1}{3}\times3\), which simplifies to \(3\leq q-1\).
Then add \(1\) to both sides: \(3 + 1\leq q-1+1\), so \(q\geq4\).

Step2: Graph the solution

The inequality \(q\geq4\) means that \(q\) can take values starting from \(4\) and going to infinity. On the number - line, we use a closed circle at \(4\) (because \(q = 4\) is included in the solution set, since the inequality is \(\geq\)) and draw a ray to the right.

Answer:

The solution of the inequality \(1\leq\frac{q - 1}{3}\) is \(q\geq4\). On the number - line, we plot a closed circle at \(4\) and draw a ray extending to the right.