Solve the compound inequality.
\[
3 x-1 \leq-10 \text { and } 2 x+6 \geq-6
\]

Graph the solution on the number line.

Step 1 ：Solve the inequality \(3x - 1 \leq -10\). Add 1 to both sides to isolate the term with x: \(3x \leq -10 + 1\)

Step 2 ：Simplify to get \(3x \leq -9\)

Step 3 ：Divide both sides by 3 to solve for x: \(x \leq -9/3\)

Step 4 ：\(\boxed{x \leq -3}\)

Step 5 ：Solve the inequality \(2x + 6 \geq -6\). Subtract 6 from both sides to isolate the term with x: \(2x \geq -6 - 6\)

Step 6 ：Simplify to get \(2x \geq -12\)

Step 7 ：Divide both sides by 2 to solve for x: \(x \geq -12/2\)

Step 8 ：\(\boxed{x \geq -6}\)

Step 9 ：The solution to the compound inequality is \(x \leq -3\) and \(x \geq -6\)

Step 10 ：To graph this on a number line, draw a closed circle at -6 and -3. Then, shade the region between -6 and -3

Step 11 ：Check the solution by substituting a number from the shaded region into the original inequalities. For example, if we choose -4, we find that both inequalities are true, so the solution is correct