Question

solve the compound inequality. -20 < 3x - 2 ≤ 1. graph the solution on the number line.

Explanation:

Step1: Solve left - hand side of inequality

Add 2 to both sides of $-20<3x - 2$:
$-20 + 2<3x-2 + 2$, which simplifies to $-18<3x$. Then divide both sides by 3: $\frac{-18}{3}<\frac{3x}{3}$, so $- 6

Step2: Solve right - hand side of inequality

Add 2 to both sides of $3x - 2\leq1$:
$3x-2 + 2\leq1 + 2$, which simplifies to $3x\leq3$. Then divide both sides by 3: $\frac{3x}{3}\leq\frac{3}{3}$, so $x\leq1$.

Answer:

The solution of the compound inequality is $-6 < x\leq1$. On the number - line, we use an open circle at $x=-6$ (because $x$ is greater than - 6, not equal to) and a closed circle at $x = 1$ (because $x$ is less than or equal to 1), and shade the region between them.