Solve for m.

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

1 answer

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:

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