Question

solve the inequality and graph the solution on the line provided.
$-16 + 5x < -26$
answer attempt 1 out of 2
$quad leqquad geqquad \text{or}$
inequality notation:
number line:
number line with ticks at -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12; left/right arrows; click and drag to plot line.
submit answer

Explanation:

Step1: Add 16 to both sides

To isolate the term with \(x\), we add 16 to both sides of the inequality \(-16 + 5x < -26\). This gives us \(-16 + 16 + 5x < -26 + 16\), which simplifies to \(5x < -10\).

Step2: Divide by 5

Next, we divide both sides of the inequality \(5x < -10\) by 5. Since 5 is a positive number, the direction of the inequality sign remains the same. So we have \(\frac{5x}{5} < \frac{-10}{5}\), which simplifies to \(x < -2\).

Answer:

Inequality Notation: \(x < -2\)
For the number line: We would draw an open circle at \(-2\) (since the inequality is strict, \(x\) is not equal to \(-2\)) and shade the region to the left of \(-2\) to represent all values of \(x\) that are less than \(-2\).