Question

solve for x and graph the solution on the number line below. -3x - 2 ≤ -29 and -35 < -3x - 2

Explanation:

Step1: Solve the first inequality

Add \(2\) to both sides of \(-3x - 2\leq - 29\):
\(-3x-2 + 2\leq -29 + 2\), which simplifies to \(-3x\leq - 27\).
Divide both sides by \(-3\) (and reverse the inequality sign because we are dividing by a negative number):
\(x\geq\frac{-27}{-3}\), so \(x\geq9\).

Step2: Solve the second inequality

Add \(2\) to both sides of \(-35\lt -3x - 2\):
\(-35 + 2\lt -3x-2 + 2\), which simplifies to \(-33\lt -3x\).
Divide both sides by \(-3\) (and reverse the inequality sign):
\(x\lt\frac{-33}{-3}\), so \(x\lt11\).

Answer:

The solution of the compound - inequality is \(9\leq x\lt11\). On the number - line, we draw a closed circle at \(x = 9\) (because \(x\) can be equal to \(9\)) and an open circle at \(x = 11\) (because \(x\) cannot be equal to \(11\)) and connect the two points with a line segment.