The inequality in the image is:

$\frac{a - 2}{3} > a + 4$

Let's solve this inequality step by step.

Step 1: Eliminate the denominator by multiplying both sides by 3.

$a - 2 > 3(a + 4)$

Step 2: Distribute the 3 on the right side.

$a - 2 > 3a + 12$

Step 3: Get all terms involving $a$ on one side by subtracting $a$ from both sides.

$-2 > 2a + 12$

Step 4: Isolate the term involving $a$ by subtracting 12 from both sides.

$-14 > 2a$

Step 5: Solve for $a$ by dividing both sides by 2.

$-7 > a$

Or equivalently,

$a < -7$

Solution:

The solution to the inequality is $a < -7$.

Would you like more details, or do you have any questions?

Here are some related questions to deepen your understanding:

1. What happens if the inequality were $\frac{a - 2}{3} \geq a + 4$?
2. Can you explain why multiplying by 3 didn't reverse the inequality?
3. How would the steps differ if we had $\frac{2 - a}{3} > a + 4$?
4. Can you solve the inequality graphically to visualize the solution?
5. What if the inequality involved absolute values, like $\frac{|a - 2|}{3} > a + 4$?

Tip: Always check if multiplying or dividing by a negative number during inequality solving reverses the inequality sign!