Question

Solve for g.
12<g+10<13
Write your answer as a compound inequality with integers.

Answer 1

To solve the compound inequality \( 12 < g + 10 < 13 \), we can break it into two parts:

1. \( 12 < g + 10 \)
2. \( g + 10 < 13 \)

Let's solve each part step-by-step:

1. **Solving \( 12 < g + 10 \)**:
\[
12 - 10 < g
\]
\[
2 < g
\]
or equivalently,
\[
g > 2
\]

2. **Solving \( g + 10 < 13 \)**:
\[
g < 13 - 10
\]
\[
g < 3
\]

Now, we can combine the results from both parts:

\[
2 < g < 3
\]

In integer form, \( g \) must be greater than 2 and less than 3. Since there are no integers between 2 and 3, we can express the solution as:

\[
g \in (2, 3) \quad \text{(there are no integers that satisfy this)}
\]

Thus, in integers, there are no solutions for \( g \). The compound inequality is:

\[
g > 2 \quad \text{and} \quad g < 3
\]

This indicates that there are no integer solutions.