Solve the inequality.
 
5(3 − x) − 4(2 − 3x) > 3

To solve the inequality \(5(3 - x) - 4(2 - 3x) > 3\), follow these steps:

1. **Distribute** the constants across the terms inside the parentheses:
   \[
   5(3 - x) = 15 - 5x
   \]
   \[
   -4(2 - 3x) = -8 + 12x
   \]
   Substituting these into the inequality gives:
   \[
   15 - 5x - 8 + 12x > 3
   \]

2. **Combine like terms** on the left-hand side:
   \[
   (15 - 8) + (-5x + 12x) > 3
   \]
   Simplifying:
   \[
   7 + 7x > 3
   \]

3. **Isolate** \(x\) by subtracting 7 from both sides:
   \[
   7x > 3 - 7
   \]
   \[
   7x > -4
   \]

4. **Solve for** \(x\) by dividing both sides by 7:
   \[
   x > \frac{-4}{7}
   \]

So, the solution is \(x > -\frac{4}{7}\).

### Do you have any questions or would you like more details on any step?

Here are 5 related questions to explore further:
1. How would the solution change if the inequality were \(5(3 - x) - 4(2 - 3x) \geq 3\)?
2. What does the solution \(x > -\frac{4}{7}\) look like on a number line?
3. How would you solve a similar inequality with more terms or different coefficients?
4. Can you verify the solution by substituting a value greater than \(-\frac{4}{7}\) into the original inequality?
5. How would the inequality change if you switched the signs in front of the parentheses?

**Tip:** After solving an inequality, it's a good idea to check your solution by substituting a value that satisfies the inequality back into the original expression.

Learn how to solve the inequality 5(3 - x) - 4(2 - 3x) > 3 with detailed steps and explanations. This problem involves inequalities, distributive property, and combining like terms. Suitable for high school students.

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