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!