Question

Solve for m.
10≥m+11≥–5
Write your answer as a compound inequality with integers.

Answer 1

To solve the compound inequality \( 10 \geq m + 11 \geq -5 \), we can break it down into two separate inequalities:

1. \( 10 \geq m + 11 \)
2. \( m + 11 \geq -5 \)

### Step 1: Solve the first inequality

Starting with the first inequality:

\[
10 \geq m + 11
\]

We can isolate \( m \) by subtracting 11 from both sides:

\[
10 - 11 \geq m
\]

\[
-1 \geq m
\]

This can be rewritten as:

\[
m \leq -1
\]

### Step 2: Solve the second inequality

Now, let's solve the second inequality:

\[
m + 11 \geq -5
\]

Again, we will isolate \( m \) by subtracting 11 from both sides:

\[
m \geq -5 - 11
\]

\[
m \geq -16
\]

### Step 3: Combine the inequalities

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

\[
-16 \leq m \leq -1
\]

### Final Answer

The solution as a compound inequality is:

\[
-16 \leq m \leq -1
\]

This represents all integer values of \( m \) that satisfy the inequality. Therefore, the integer solutions are:

\[
m \in \{-16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1\}
\]