Question

solve the inequality.
-6.2 < 2n + 8.6 < 21.4
solution: -7.4 < n < 6.4
graph the solution.

Explanation:

Step1: Subtract 8.6 from all parts

To isolate the term with \( n \), we subtract 8.6 from each part of the compound inequality.
\[
-6.2 - 8.6 < 2n + 8.6 - 8.6 < 21.4 - 8.6
\]
Calculating each part: \( -6.2 - 8.6 = -14.8 \), \( 2n + 8.6 - 8.6 = 2n \), and \( 21.4 - 8.6 = 12.8 \). So we get:
\[
-14.8 < 2n < 12.8
\]

Step2: Divide all parts by 2

To solve for \( n \), we divide each part of the inequality by 2.
\[
\frac{-14.8}{2} < \frac{2n}{2} < \frac{12.8}{2}
\]
Calculating each part: \( \frac{-14.8}{2} = -7.4 \), \( \frac{2n}{2} = n \), and \( \frac{12.8}{2} = 6.4 \). So the solution is:
\[
-7.4 < n < 6.4
\]

Answer:

The solution to the inequality \( -6.2 < 2n + 8.6 < 21.4 \) is \( -7.4 < n < 6.4 \). To graph this, we use an open circle at \( -7.4 \) and \( 6.4 \) (since the inequality is strict, \( < \) not \( \leq \)) and shade the region between them on the number line.