Let's solve the inequality step by step:

1. Starting with the given inequality:

$3x + 2 > 8 + x$

2. Subtract $x$ from both sides to move all the $x$-terms to the left-hand side:

$3x - x + 2 > 8$ $2x + 2 > 8$

3. Now, subtract 2 from both sides to isolate the $2x$ term:

$2x > 6$

4. Finally, divide both sides by 2 to solve for $x$:

$x > 3$

Solution:

The solution to the inequality is: $x > 3$

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Would you like more details on how to solve inequalities?

Here are 5 related questions for further practice:

1. Solve: $4x - 5 \leq 3x + 2$
2. Solve: $2x + 7 > 3x - 1$
3. Solve the system of inequalities: $x + 4 \leq 7$ and $x - 2 > 3$
4. Solve: $5(x - 3) \geq 2(2x + 1)$
5. How do you solve an inequality with a fraction like $\frac{x}{4} \leq 2$?

Tip: Always remember to reverse the inequality sign when multiplying or dividing both sides by a negative number.