Question

Solve for n.
–
13<20n+7<7
Write your answer as a compound inequality with integers.

Answer 1

To solve the compound inequality \(-13 < 20n + 7 < 7\), we'll break it into two parts and solve each part separately.

1. **First part:**
\[
-13 < 20n + 7
\]
Subtract 7 from both sides:
\[
-13 - 7 < 20n
\]
\[
-20 < 20n
\]
Now divide by 20:
\[
-1 < n \quad \text{or} \quad n > -1
\]

2. **Second part:**
\[
20n + 7 < 7
\]
Subtract 7 from both sides:
\[
20n < 7 - 7
\]
\[
20n < 0
\]
Now divide by 20:
\[
n < 0
\]

Now we combine the results from both parts:
\[
-1 < n < 0
\]

The solution as a compound inequality with integers is:
\[
n \in (-1, 0)
\]

In terms of integers, this means:
\[
n = -1 \quad (\text{not included}) \text{ and } n = 0 \quad (\text{not included})
\]
Thus, there are no integers \( n \) that satisfy the solution.