Question

Solve each compound inequality.
5 < k - 2 < 11

Answer 1

To solve the compound inequality \( 5 < k - 2 < 11 \), we can break it down into two separate inequalities:

1. \( 5 < k - 2 \)
2. \( k - 2 < 11 \)

Let's solve the first inequality:

1. \( 5 < k - 2 \)

Add 2 to both sides:

\[
5 + 2 < k
\]
\[
7 < k
\]

This can be written as:

\[
k > 7
\]

Now, let's solve the second inequality:

2. \( k - 2 < 11 \)

Add 2 to both sides:

\[
k < 11 + 2
\]
\[
k < 13
\]

Now we combine the results from both inequalities. We have:

\[
7 < k < 13
\]

So the solution to the compound inequality is:

\[
k \in (7, 13)
\]

This means \( k \) is greater than 7 and less than 13.