Let's solve the inequality:

Given inequality: $3(x + 5) < 2(x + 2) + 8$

Step 1: Expand both sides

On the left-hand side: $3(x + 5) = 3x + 15$

On the right-hand side: $2(x + 2) + 8 = 2x + 4 + 8 = 2x + 12$

So the inequality becomes: $3x + 15 < 2x + 12$

Step 2: Move the variables to one side

Subtract $2x$ from both sides: $3x - 2x + 15 < 12$ This simplifies to: $x + 15 < 12$

Step 3: Solve for $x$

Subtract 15 from both sides: $x < 12 - 15$ $x < -3$

Final solution:

$x < -3$

Let me know if you need more details or have any questions!

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Here are 5 related questions for further practice:

1. Solve $5(x + 2) \geq 3(x + 4) + 7$.
2. Solve $4x - 7 < 2x + 5$.
3. Solve the compound inequality $2x + 1 < 5x + 7 < 8x + 12$.
4. Solve $7(x - 1) > 4x + 5$.
5. Solve $6x + 9 \leq 2(x + 4) + 13$.

Tip: Always simplify both sides of the inequality before moving variables and constants around.