Solve for n.

Question

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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.