Question

solve for ( x ) and graph the solution on the number line below.
-32 < -3x + 4 leq 16
answer attempt 1 out of 2
inequality notation:
number line:

Explanation:

Step1: Subtract 4 from all parts

$$\begin{align*} -32 - 4&< -3x+4 - 4\leq16 - 4\\ -36&< -3x\leq12 \end{align*}$$

Step2: Divide all parts by -3 (reverse inequalities)

$$\begin{align*} \frac{-36}{-3}&> \frac{-3x}{-3}\geq\frac{12}{-3}\\ 12&>x\geq - 4 \end{align*}$$

Answer:

Inequality Notation: $-4\leq x<12$

For the number - line: Plot a closed circle at $x = - 4$ (since $x$ can be equal to $-4$) and an open circle at $x = 12$ (since $x$ is less than $12$) and draw a line segment connecting them.