Let's solve the inequality step by step:

### Given inequality:
\[
8(x - 2) + 9 < 3(x - 1) + 5x
\]

### Step 1: Distribute the constants inside the parentheses.
\[
8x - 16 + 9 < 3x - 3 + 5x
\]

### Step 2: Simplify both sides.
\[
8x - 7 < 8x - 3
\]

### Step 3: Subtract \(8x\) from both sides to eliminate the \(x\)-terms on both sides.
\[
-7 < -3
\]

### Step 4: Analyze the result.
The inequality \(-7 < -3\) is always **true**, which means the original inequality holds for **all values of \(x\)**.

### Conclusion:
The solution is that \(x\) can be any real number:
\[
x \in (-\infty, \infty)
\]

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

Here are some related questions for further practice:
1. Solve \(5(x + 1) > 2(x - 3) + 7\).
2. Solve \(7x + 4 \leq 3(2x - 5) + 2x\).
3. Solve \(9 - 4(x - 2) > 6x + 8\).
4. Solve \(10x - 3 \geq 3(4x - 1) + 2\).
5. Solve \(6x - (2x + 3) < 4x + 7\).

**Tip:** Always simplify expressions on both sides of an equation or inequality before solving.

Learn how to solve the linear inequality 8(x-2) + 9 < 3(x-1) + 5x with a detailed step-by-step solution. This problem covers algebraic concepts such as the distributive property and simplifying inequalities. Suitable for students in Grades 8-10.

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