https://file.aiquickdraw.com/mathbot/file/1725477526321uczphlnv.jpg

The image contains a system of inequalities:

\[
\begin{cases}
2(3 - 2x) > 8 - 5x, \\
10 - x > 2.
\end{cases}
\]

### Let's solve each inequality step by step:

#### First Inequality: \( 2(3 - 2x) > 8 - 5x \)

1. Distribute the \( 2 \) on the left side:
   \[
   6 - 4x > 8 - 5x
   \]

2. Add \( 5x \) to both sides to get all terms involving \( x \) on one side:
   \[
   6 + x > 8
   \]

3. Subtract \( 6 \) from both sides:
   \[
   x > 2
   \]

#### Second Inequality: \( 10 - x > 2 \)

1. Subtract \( 10 \) from both sides:
   \[
   -x > -8
   \]

2. Multiply both sides by \( -1 \) (and remember to flip the inequality sign):
   \[
   x < 8
   \]

### Final Answer:
The solution to the system of inequalities is:

\[
2 < x < 8
\]

This means \( x \) is in the interval \( (2, 8) \).

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

### Related Questions:
1. How would the solution change if one inequality was \( \geq \) instead of \( > \)?
2. What happens if both inequalities had the sign \( \leq \)?
3. How can you graph the solution set on a number line?
4. Can you solve a similar system of inequalities with a quadratic inequality involved?
5. What is the impact of multiplying an inequality by a negative number?

### Tip:
When solving inequalities, always remember to flip the inequality sign if you multiply or divide both sides by a negative number.

Solve the system of inequalities: 2(3 - 2x) > 8 - 5x and 10 - x > 2.

This guide walks you through solving the system of inequalities 2(3 - 2x) > 8 - 5x and 10 - x > 2 step by step. Learn the core concepts of algebra, such as the distributive property and solving linear inequalities, essential for students in Grades 7-9.

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