https://file.aiquickdraw.com/mathbot/file/1725587851624959bkb48.jpg

Let's solve the inequality and graph the solution as required.

The inequality is:

\[
-10 + 3x \geq -16
\]

### Step-by-step solution:

1. **Isolate \(3x\):**

\[
3x \geq -16 + 10
\]
\[
3x \geq -6
\]

2. **Solve for \(x\):**

\[
x \geq \frac{-6}{3}
\]
\[
x \geq -2
\]

### Inequality Notation:
The inequality notation is:

\[
x \geq -2
\]

### Graphing on the Number Line:
- You would plot a closed circle at \(-2\) because the inequality includes \(\geq\).
- The line will extend to the right (positive infinity), as \(x\) is greater than or equal to \(-2\).

Would you like more details or clarifications on any step?

Here are five related questions to expand on this topic:

1. How do we solve compound inequalities with multiple steps?
2. What is the difference between solving linear inequalities and equations?
3. How do you graph solutions when the inequality is strict (e.g., \(<\) or \(>\))?
4. How does dividing or multiplying by a negative number affect an inequality?
5. Can you provide examples of word problems involving inequalities?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing by a negative number in inequality problems.

Solve the inequality and graph the solution on the line provided: -10 + 3x ≥ -16

Learn how to solve the linear inequality -10 + 3x ≥ -16 and graph the solution on a number line. This problem involves key algebraic concepts such as isolating variables and understanding inequality properties, suitable for students in Grades 6-8.

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