Question

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

Explanation:

Step1: Solve the first inequality

Add 1 to both sides of $2x - 1\leq - 1$. We get $2x-1 + 1\leq - 1+1$, which simplifies to $2x\leq0$. Then divide both sides by 2: $x\leq0$.

Step2: Solve the second inequality

Subtract 2 from both sides of $3x + 2\geq20$. We have $3x+2 - 2\geq20 - 2$, which simplifies to $3x\geq18$. Then divide both sides by 3: $x\geq6$.

Answer:

The solution of the compound - inequality is $x\leq0$ or $x\geq6$. On the number - line, we draw a closed circle at 0 and shade to the left for $x\leq0$, and draw a closed circle at 6 and shade to the right for $x\geq6$.