Question

solve the inequality and graph the solution.
19n ≤ 38
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.
-5 -4 -3 -2 -1 0 1 2 3 4 5
submit

Explanation:

Step1: Isolate the variable n

To solve the inequality \(19n \leq 38\), we divide both sides of the inequality by 19.

$$ \frac{19n}{19} \leq \frac{38}{19} $$

Step2: Simplify both sides

Simplifying the left side gives \(n\) (since \(\frac{19n}{19}=n\)) and simplifying the right side gives 2 (since \(\frac{38}{19} = 2\)). So we have \(n \leq 2\).

For graphing:

• We have a closed circle at 2 (because the inequality is "less than or equal to", so 2 is included in the solution set).
• Then we draw a line to the left of 2 (since \(n\) can be any number less than or equal to 2) on the number line.

Answer:

The solution to the inequality \(19n \leq 38\) is \(n \leq 2\). For the graph, place a closed circle at 2 and draw a ray extending to the left from 2.