Question

solve for x and graph the solution on the number line below.
1 ≥ -x - 1 and -x - 1 ≥ -13
answer attempt 1 out of 2
< > ≤ ≥ or
inequality notation:
number line:
submit answer

Explanation:

Step1: Solve the first inequality \(1\geq -x - 1\)

Add \(1\) to both sides: \(1+1\geq -x-1 + 1\), so \(2\geq -x\). Multiply both sides by \(- 1\) (and reverse the inequality sign): \(x\geq - 2\).

Step2: Solve the second inequality \(-x - 1\geq -13\)

Add \(1\) to both sides: \(-x-1 + 1\geq -13 + 1\), so \(-x\geq -12\). Multiply both sides by \(-1\) (and reverse the inequality sign): \(x\leq12\).

Answer:

The solution in inequality notation is \(-2\leq x\leq12\). On the number - line, we draw a closed circle at \(-2\) (because \(x = - 2\) is included in the solution set, due to the \(\geq\) sign) and a closed circle at \(12\) (because \(x = 12\) is included in the solution set, due to the \(\leq\) sign), and then connect the two points with a line segment.