Let's solve the inequality step by step:

### Inequality:
\[
0.6x - 14 - 1.6x < 20
\]

1. Combine like terms:
\[
(0.6x - 1.6x) - 14 < 20
\]
\[
-1.0x - 14 < 20
\]

2. Add 14 to both sides to isolate the term with \(x\):
\[
-1.0x < 20 + 14
\]
\[
-1.0x < 34
\]

3. Divide both sides by \(-1.0\). Remember, when you divide by a negative number, you must reverse the inequality sign:
\[
x > \frac{34}{-1.0}
\]
\[
x > -34
\]

### Final solution:
\[
x > -34
\]

Let me know if you'd like any clarifications or further details!

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Here are 5 related questions you could explore:
1. How do you solve inequalities involving absolute values?
2. How does dividing or multiplying by negative numbers affect inequalities?
3. What is the difference between solving an equation and an inequality?
4. Can you graph the solution of \(x > -34\) on a number line?
5. How would the inequality change if it was \(0.6x - 14 - 1.6x \leq 20\)?

**Tip:** When solving inequalities, always remember to reverse the inequality sign when multiplying or dividing by a negative number!

Learn how to solve the linear inequality 0.6x - 14 - 1.6x < 20 with a step-by-step guide. This problem explores key algebraic concepts such as combining like terms and understanding how dividing by negative numbers affects inequalities. Ideal for students in Grades 7-9.

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