https://file.aiquickdraw.com/mathbot/file/1727309531839hze9klij.jpg

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!

Learn how to solve the linear inequality (a - 2)/3 > a + 4 with a detailed step-by-step solution. This problem involves key algebraic concepts such as solving inequalities and distributing terms. Suitable for students in Grades 8-10.

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