solve for x and graph the solution on the number line below. if possible, resolve your answer to a single…

solve for x and graph the solution on the number line below. if possible, resolve your answer to a single inequality. in case of no solution (∅), leave the number line blank. -27 ≥ -3x - 9 or -39 ≤ -3x - 9 answer < > ≤ ≥ or ∅ r inequality notation: number line:

solve for x and graph the solution on the number line below. if possible, resolve your answer to a single inequality. in case of no solution (∅), leave the number line blank. -27 ≥ -3x - 9 or -39 ≤ -3x - 9 answer < > ≤ ≥ or ∅ r inequality notation: number line:

Answer

Explanation:

Step1: Solve the first inequality

Add (9) to both sides of (-27\geq - 3x-9): (-27 + 9\geq-3x-9 + 9), which simplifies to (-18\geq - 3x). Divide both sides by (-3) (and reverse the inequality sign because we are dividing by a negative number): (\frac{-18}{-3}\leq\frac{-3x}{-3}), so (x\geq6).

Step2: Solve the second inequality

Add (9) to both sides of (-39\leq - 3x-9): (-39 + 9\leq-3x-9 + 9), which simplifies to (-30\leq - 3x). Divide both sides by (-3) (and reverse the inequality sign): (\frac{-30}{-3}\geq\frac{-3x}{-3}), so (x\leq10).

Answer:

(x\geq6) or (x\leq10) (which is equivalent to (x\in R) since all real numbers satisfy either (x\geq6) or (x\leq10) or both). So the inequality notation is (x\in R). On the number - line, you would shade the entire line.