Question

question solve for x and graph the solution on the number line below. -x - 5 ≥ 1 or -x - 5 < -8 answer attempt 2 out of 2 < > inequality notation: -6 ≤ x > 3 number line:

Explanation:

Step1: Solve the first inequality

Solve \(-x - 5\geq1\).
Add \(5\) to both sides: \(-x-5 + 5\geq1 + 5\), which simplifies to \(-x\geq6\).
Multiply both sides by \(- 1\) and reverse the inequality sign: \(x\leq - 6\).

Step2: Solve the second inequality

Solve \(-x - 5\lt - 8\).
Add \(5\) to both sides: \(-x-5 + 5\lt - 8+5\), which simplifies to \(-x\lt - 3\).
Multiply both sides by \(-1\) and reverse the inequality sign: \(x\gt3\).

Answer:

The solution is \(x\leq - 6\) or \(x\gt3\). On the number - line, for \(x\leq - 6\), we have a closed circle at \(-6\) (since the inequality is \(\leq\)) and an arrow pointing to the left. For \(x\gt3\), we have an open circle at \(3\) (since the inequality is \(\gt\)) and an arrow pointing to the right.