Question

solve for $x$ and graph the solution on the number line below.
$19\leq - 5x + 4 < 54$
answer
inequality notation:
number line:

Explanation:

Step1: Subtract 4 from all parts

$$\begin{align*} 19 - 4&\leq - 5x+4 - 4<54 - 4\\ 15&\leq - 5x<50 \end{align*}$$

Step2: Divide all parts by -5 (reverse inequalities)

$$\begin{align*} \frac{15}{-5}&\geq\frac{-5x}{-5}>\frac{50}{-5}\\ - 3&\geq x>-10 \end{align*}$$

Answer:

Inequality Notation: \(-10 < x\leq - 3\)

To graph on the number line: Place an open circle at \(-10\) (because \(x>-10\), not equal to \(-10\)) and a closed circle at \(-3\) (because \(x\leq - 3\)), then shade the region between them.