Question

directions - graph the compound inequality: x ≥ 0 and x ≤ 10

Explanation:

Step1: Analyze the inequality \(x\geq0\)

For \(x\geq0\), we place a closed - circle at \(x = 0\) (because the inequality includes equality) and shade to the right of \(0\) on the number line.

Step2: Analyze the inequality \(x\leq10\)

For \(x\leq10\), we place a closed - circle at \(x = 10\) (because the inequality includes equality) and shade to the left of \(10\) on the number line.

Step3: Combine the two inequalities

Since it is a compound inequality \(x\geq0\) and \(x\leq10\), we take the intersection of the two shaded regions. The intersection is the region between \(x = 0\) and \(x = 10\) (including both endpoints).

Answer:

Place a closed - circle at \(0\), a closed - circle at \(10\), and shade the region between \(0\) and \(10\) on the number line.