Question

solve the compound inequality.
2x - 1 ≥ - 11 and 2x - 5 ≤ - 5
graph the solution on the number line.

Explanation:

Step1: Solve the first inequality

Add 1 to both sides of $2x - 1\geq - 11$:
$2x-1 + 1\geq - 11+1$, which simplifies to $2x\geq - 10$. Then divide both sides by 2: $x\geq - 5$.

Step2: Solve the second inequality

Add 5 to both sides of $2x - 5\leq - 5$:
$2x-5 + 5\leq - 5+5$, which simplifies to $2x\leq0$. Then divide both sides by 2: $x\leq0$.

Answer:

The solution of the compound - inequality is $-5\leq x\leq0$. On the number - line, we use a closed circle at $x = - 5$ and $x = 0$ and draw a line segment between them.