Question

name: pedro solve each problem and graph the 1) |20x|-8≥72

Explanation:

Step1: Isolate the absolute - value term

Add 8 to both sides of the inequality \(|20x|-8\geq72\).
\(|20x|-8 + 8\geq72 + 8\), so \(|20x|\geq80\).

Step2: Consider two cases

Case 1: When \(20x\geq0\) (i.e., \(x\geq0\)), the inequality becomes \(20x\geq80\). Divide both sides by 20: \(\frac{20x}{20}\geq\frac{80}{20}\), so \(x\geq4\).
Case 2: When \(20x<0\) (i.e., \(x < 0\)), the inequality \(|20x|\geq80\) becomes \(-20x\geq80\). Divide both sides by - 20. When dividing an inequality by a negative number, the direction of the inequality sign changes. So \(\frac{-20x}{-20}\leq\frac{80}{-20}\), and \(x\leq - 4\).

Answer:

The solution of the inequality \(|20x|-8\geq72\) is \(x\leq - 4\) or \(x\geq4\). On the number - line, we mark a closed circle at \(x=-4\) and shade to the left, and mark a closed circle at \(x = 4\) and shade to the right.