Step 1: Solve the Inequality

Given inequality:

$2a + 10 > 2$

Subtract 10 from both sides:

$2a + 10 - 10 > 2 - 10$

$2a > -8$

Divide both sides by 2:

$\frac{2a}{2} > \frac{-8}{2}$

$a > -4$

Step 2: Graph the Solution

To graph the solution $a > -4$:

1. Draw a number line.
2. Mark the point $-4$ on the line.
3. Use an open circle at $-4$ to indicate that $-4$ is not included in the solution (since the inequality is strict: $>$).
4. Shade the line to the right of $-4$ to represent all values greater than $-4$.

Visual Representation of the Solution

The graph would look like this:

--------(----|================>
          -4 

The open circle at $-4$ and shading to the right show all values of $a$ that are greater than $-4$.

Would you like more details or have any questions?

Related Questions:

1. How would the graph change if the inequality were $a \geq -4$?
2. What happens if the inequality were $2a + 10 < 2$?
3. How do you solve and graph compound inequalities like $2a + 10 > 2$ and $a < 5$?
4. How would you graph the inequality on a coordinate plane?
5. What are some real-world examples where inequalities like this are used?

Tip: Always double-check which direction the inequality symbol points when graphing!