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 4
inequality notation:
number line:
touch and drag to plot line.

Explanation:

Step1: Solve \(-x - 5 \geq 1\)

Add 5 to both sides: \(-x - 5 + 5 \geq 1 + 5\)
Simplify: \(-x \geq 6\)
Multiply both sides by -1 (reverse inequality): \(x \leq -6\)

Step2: Solve \(-x - 5 < -8\)

Add 5 to both sides: \(-x - 5 + 5 < -8 + 5\)
Simplify: \(-x < -3\)
Multiply both sides by -1 (reverse inequality): \(x > 3\)

Step3: Combine solutions

The solution is \(x \leq -6\) or \(x > 3\)

Answer:

Inequality Notation: \(x \leq -6\) or \(x > 3\)

For the number line:

• For \(x \leq -6\), draw a closed circle at \(-6\) and shade to the left.
• For \(x > 3\), draw an open circle at \(3\) and shade to the right.