We are tasked with solving the inequality:

$2x + 7 > 3$

Step-by-Step Solution:

1. Isolate $x$: To solve for $x$, we first subtract 7 from both sides:

   $2x > 3 - 7$

   Simplifying the right-hand side:

   $2x > -4$

2. Solve for $x$: Now, divide both sides by 2 to isolate $x$:

   $x > \frac{-4}{2}$

   Simplifying:

   $x > -2$

Solution in Interval Notation:

The solution to the inequality $x > -2$ can be written in interval notation as:

$(-2, \infty)$

Illustration on the Real Number Line:

• Draw a real number line.
• Mark a hollow circle at $-2$ (since $x = -2$ is not included in the solution).
• Shade the region to the right of $-2$, representing all values greater than $-2$.

Would you like the detailed steps for graphing, or do you have any questions? Here are some related questions you might explore:

1. How do you solve inequalities with multiple steps?
2. How do you handle inequalities that involve division by a negative number?
3. What is the difference between strict and non-strict inequalities?
4. How do you solve compound inequalities?
5. How can absolute value inequalities be solved?

Tip: Always remember that when dividing or multiplying both sides of an inequality by a negative number, you must reverse the inequality sign.