Which of the following number lines represents the solution set to the following inequality?   x+4>2

Let's start by solving the given inequality:

\[
x + 4 > 2
\]

### Step 1: Isolate \(x\)
To isolate \(x\), subtract 4 from both sides:

\[
x + 4 - 4 > 2 - 4
\]

\[
x > -2
\]

### Solution
The inequality \(x > -2\) means that \(x\) is any number greater than \(-2\), but not equal to \(-2\). This would be represented on a number line with an open circle at \(-2\) (indicating that \(-2\) is not included in the solution set) and a line extending to the right to indicate all values greater than \(-2\).

The number line that represents this solution set would have:
- An open circle at \(-2\),
- A shaded region to the right of \(-2\), covering all numbers greater than \(-2\).

### Do you have any further questions, or would you like more details on this?

Here are 5 related questions to explore further:
1. What would the solution look like if the inequality were \(x + 4 \geq 2\)?
2. How do we represent inequalities on a number line with "less than" instead of "greater than"?
3. What changes if the inequality involves a negative variable, like \(-x + 4 > 2\)?
4. How would you solve an inequality like \(2x + 4 > 8\)?
5. What are the different methods to solve inequalities, and when should each be used?

**Tip:** Always check whether you need to reverse the inequality sign when multiplying or dividing both sides by a negative number!

Which of the following number lines represents the solution set to the following inequality? x+4>2

Learn how to solve the inequality x + 4 > 2 and represent the solution on a number line. This problem explores key algebraic concepts, including isolating variables in inequalities and visualizing solutions. Suitable for students in Grades 6-8.

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