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