Question

Solve for m.
–16<m+36≤100
Write your answer as a compound inequality with integers, proper fractions, and improper fractions in simplest form.

Answer 1

To solve the compound inequality \(-16 < m + 36 \leq 100\), we will break it down into two parts:

1. \(-16 < m + 36\)
2. \(m + 36 \leq 100\)

### Step 1: Solve the first inequality

\[
-16 < m + 36
\]

Subtract 36 from both sides:

\[
-16 - 36 < m
\]

\[
-52 < m
\]

This can be rewritten as:

\[
m > -52
\]

### Step 2: Solve the second inequality

\[
m + 36 \leq 100
\]

Subtract 36 from both sides:

\[
m \leq 100 - 36
\]

\[
m \leq 64
\]

### Step 3: Combine the results

Now we combine the two results:

\[
-52 < m \leq 64
\]

### Final Answer:

So the solution as a compound inequality is:

\[
-52 < m \leq 64
\]

This means \(m\) can take any value greater than \(-52\) and up to and including \(64\).