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Let's solve the inequality step by step:

### Given Inequality:
\[
7m + 11 \geq -31
\]

### Step 1: Subtract 11 from both sides
To isolate the term with \(m\), first subtract 11 from both sides:
\[
7m + 11 - 11 \geq -31 - 11
\]
\[
7m \geq -42
\]

### Step 2: Divide both sides by 7
Now, divide both sides of the inequality by 7 to solve for \(m\):
\[
\frac{7m}{7} \geq \frac{-42}{7}
\]
\[
m \geq -6
\]

### Final Solution:
\[
m \geq -6
\]

The solution is \( m \geq -6 \). This means any value of \(m\) greater than or equal to \(-6\) satisfies the inequality.

Would you like further details or have any questions?

### Related Questions:
1. What is the difference between solving inequalities and equations?
2. How would the solution change if it were \(7m + 11 \leq -31\)?
3. Can you solve a similar inequality with fractions, like \( \frac{5m + 3}{2} \geq 7\)?
4. How would you solve an inequality involving absolute values, such as \( |7m + 11| \geq 31\)?
5. How can graphing the solution on a number line help visualize the inequality?

### Tip:
Always reverse the inequality symbol when multiplying or dividing by a negative number in inequality problems.

Learn how to solve the linear inequality 7m + 11 ≥ -31 with a detailed, step-by-step solution. This problem covers algebraic concepts, including the manipulation of inequalities and solving for a variable. Ideal for students in Grades 7-9.

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