https://file.aiquickdraw.com/mathbot/file/17262704325660d66x6ex.jpg

Let's solve the system of inequalities from the image:

Given inequalities:
\[
\begin{cases}
10x < 2 \\
x > 0.1
\end{cases}
\]

### Step 1: Solve \( 10x < 2 \)

To solve for \( x \), divide both sides of the inequality by 10:

\[
x < \frac{2}{10} = 0.2
\]

Thus, the first inequality simplifies to:

\[
x < 0.2
\]

### Step 2: Combine with \( x > 0.1 \)

Now, we combine the two inequalities:

\[
0.1 < x < 0.2
\]

This tells us that \( x \) must be a number between 0.1 and 0.2.

### Step 3: Find any three solutions

Any number between 0.1 and 0.2 will work as a solution. Three possible values for \( x \) are:

\[
x = 0.11, \quad x = 0.15, \quad x = 0.19
\]

These are all within the valid range for \( x \).

Would you like further details or have any questions?

Here are 5 related questions for further practice:
1. What would the solution set look like if the inequality was \( 10x \leq 2 \) instead of \( 10x < 2 \)?
2. How would you solve the inequality if the second condition were \( x \geq 0.1 \) rather than \( x > 0.1 \)?
3. How do you represent the solution on a number line?
4. Can you find the interval notation for this system of inequalities?
5. What happens if we replace \( 10x < 2 \) with \( 10x > 2 \)?

**Tip:** When working with inequalities, always pay attention to whether the inequality sign includes equality (like \( \leq \) or \( \geq \))—this changes how the boundary values are treated in your solution.

Solve the system of inequalities: 10x < 2 and x > 0.1. Indicate any three solutions.

Learn how to solve the system of inequalities 10x < 2 and x > 0.1 with a detailed step-by-step solution. This problem covers key algebraic concepts and is suitable for students in Grades 7-9. Solutions include the range 0.1 < x < 0.2.

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