Question

solve for x and graph the solution on the number line below.

-x - 5 ≥ 1 or -x - 5 < -8

answer attempt 1 out of 2

< > ≤ ≥ or

inequality notation:

number line:

submit answer

Explanation:

Step1: Solve the first inequality

Solve \(-x - 5\geq1\).
Add 5 to both sides: \(-x\geq1 + 5\), so \(-x\geq6\).
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: \(-x\lt - 8+5\), so \(-x\lt - 3\).
Multiply both sides by - 1 (and reverse the inequality sign): \(x\gt3\).

Answer:

Inequality Notation: \(x\leq - 6\) or \(x\gt3\)

For the number line:

• For \(x\leq - 6\), draw a closed circle at - 6 (because the inequality includes equality) and shade to the left.
• For \(x\gt3\), draw an open circle at 3 (because the inequality does not include equality) and shade to the right.