Solve the inequality in terms of intervals and illustrate the solution set on the real number line.
$ 2x + 7 > 3 $


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.

Solve the inequality in terms of intervals and illustrate the solution set on the real number line.
$ 2x + 7 > 3 $

Learn how to solve the inequality 2x + 7 > 3 and represent the solution using interval notation. This problem covers key algebraic concepts, including inequalities and graphing on the real number line. Suitable for students in Grades 7-9.

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