Question

solve and graph the compound inequality 2x + 1 ≤ 7 and - 2x + 1 ≤ 9

Explanation:

Step1: Solve the first inequality

Subtract 1 from both sides of $2x + 1\leq7$:
$2x+1 - 1\leq7 - 1$, which simplifies to $2x\leq6$. Then divide both sides by 2: $x\leq3$.

Step2: Solve the second inequality

Subtract 1 from both sides of $-2x + 1\leq9$:
$-2x+1 - 1\leq9 - 1$, which gives $-2x\leq8$. Divide both sides by - 2 and reverse the inequality sign: $x\geq - 4$.

Step3: Determine the solution set

The solution of the compound - inequality is $-4\leq x\leq3$.

Step4: Analyze the graph

The graph of $x\geq - 4$ has a closed - circle at $x=-4$ (because the inequality is $\geq$) and the graph of $x\leq3$ has a closed - circle at $x = 3$ (because the inequality is $\leq$). The line segment between $x=-4$ and $x = 3$ is shaded.

Answer:

The third graph (the one with closed - circles at $x=-4$ and $x = 3$ and the line segment between them shaded).