Question

solve for x and graph the solution on the number line below.
-18 ≤ -x - 6 < -15
answer attempt 1 out of 3
< > ≤ ≥ or
inequality notation:
number line:

Explanation:

Step1: Add 6 to all parts

$$\begin{align*} -18 + 6&\leq -x-6 + 6< -15 + 6\\ -12&\leq -x< -9 \end{align*}$$

Step2: Multiply all parts by -1 (reverse inequalities)

$$\begin{align*} (-1)\times(-12)&\geq (-1)\times(-x)>(-1)\times(-9)\\ 12&\geq x>9 \end{align*}$$

Answer:

Inequality Notation: \(9 < x\leq12\)

For the number line: Place a closed circle at \(x = 12\) (since \(x\) can equal \(12\)) and an open circle at \(x = 9\) (since \(x\) cannot equal \(9\)), then draw a line segment connecting the two points.