Question

compound inequalities (l1) unique id: 0040 score: 2/4 penalty: none question solve for x and graph the solution on the number line below. 16 ≥ -5x - 9 ≥ -44 answer attempt 1 out of 2

Explanation:

Step1: Add 9 to all parts

To solve the compound inequality \(16 \geq -5x - 9 \geq -44\), we first add 9 to each part of the inequality. This is done to isolate the term with \(x\).
\[
16 + 9 \geq -5x - 9 + 9 \geq -44 + 9
\]
Simplifying each part:
\[
25 \geq -5x \geq -35
\]

Step2: Divide by -5 (reverse inequalities)

Next, we divide each part of the inequality by -5. When dividing or multiplying an inequality by a negative number, the direction of the inequality signs must be reversed.
\[
\frac{25}{-5} \leq \frac{-5x}{-5} \leq \frac{-35}{-5}
\]
Simplifying each part:
\[
-5 \leq x \leq 7
\]

Answer:

The solution for \(x\) is \(-5 \leq x \leq 7\). To graph this on a number line, we draw a closed circle at \(-5\) and \(7\) (since the inequality is "greater than or equal to" and "less than or equal to") and shade the region between them.