To solve the inequality \(-20 + 19x < 6x + 17\), follow these steps:

1. **Subtract \(6x\) from both sides:**
   \[
   -20 + 19x - 6x < 17
   \]
   \[
   -20 + 13x < 17
   \]

2. **Add 20 to both sides:**
   \[
   13x < 17 + 20
   \]
   \[
   13x < 37
   \]

3. **Divide both sides by 13:**
   \[
   x < \frac{37}{13}
   \]
   \[
   x < \approx 2.846
   \]

Thus, the solution to the inequality is \(x < \frac{37}{13}\), or approximately \(x < 2.846\).

Would you like more details on this solution or have any other questions?

Here are 5 related questions you might find interesting:

1. How would you solve the inequality if the signs were reversed, such as \(19x > 6x + 37\)?
2. What if there were an additional constant term on both sides of the inequality?
3. How would the solution change if you had to solve the equation \(19x = 6x + 37\) instead?
4. Can you graph the inequality and interpret the solution visually?
5. What steps are necessary if the inequality involved fractions or decimals?

**Tip:** Always check your solution by substituting values near the boundary to ensure they satisfy the original inequality.

Discover how to solve the linear inequality -20 + 19x < 6x + 17 with a step-by-step guide. This problem involves key algebraic concepts like simplification and properties of inequalities, making it ideal for students in Grades 8-10.

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