Question

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

$-32 < -3x + 4 leq 16$

answer attempt 1 out of 3

$<$
$>$<
$leq$
$geq$
$or$

inequality notation:

number line:

click and drag to plot line.

submit answer

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: $-4\leq x<12$

To graph on the number - line:

• Put a closed circle at $x = - 4$ (because the inequality includes equality for this part, $x\geq - 4$)
• Put an open circle at $x = 12$ (because the inequality is strict for this part, $x<12$)
• Draw a line segment connecting the two points.