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Let's solve the inequality:

\[
0.1x + 0.9x \geq 2.0
\]

1. Combine like terms:

\[
(0.1 + 0.9)x \geq 2.0
\]

\[
1.0x \geq 2.0
\]

2. Simplify further:

\[
x \geq \frac{2.0}{1.0}
\]

\[
x \geq 2
\]

So, the solution is:

\[
x \geq 2
\]

This means the correct answer is option **A** with the inequality \( x \geq 2 \).

Do you want further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How do we solve inequalities with fractions?
2. What happens if we divide by a negative number in an inequality?
3. Can inequalities have multiple solutions?
4. How would the solution change if the inequality symbol were \( > \) instead of \( \geq \)?
5. What is the difference between solving equalities and inequalities?

**Tip**: Always remember that when multiplying or dividing both sides of an inequality by a negative number, you must reverse the inequality sign!

Solve the inequality 0.1x + 0.9x ≥ 2.0.

Learn how to solve the linear inequality 0.1x + 0.9x ≥ 2.0 with a step-by-step explanation. This problem covers basic algebraic concepts like combining like terms and solving inequalities. Suitable for students in Grades 7-9.

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