https://file.aiquickdraw.com/mathbot/file/17269343481905g2298p4.jpg

The equation provided in the image is:

\[
1 - \frac{x + 2}{3} = - \frac{3(x - 1)}{5}
\]

### Step-by-Step Solution:

1. **Eliminate the fractions by finding the least common denominator (LCD):**
   The denominators are 3 and 5. The least common denominator is 15. We will multiply both sides of the equation by 15 to clear the fractions.

   \[
   15 \times \left( 1 - \frac{x + 2}{3} \right) = 15 \times \left( - \frac{3(x - 1)}{5} \right)
   \]

2. **Distribute the 15 across both terms on each side:**
   
   On the left-hand side:
   \[
   15 \times 1 - 15 \times \frac{x + 2}{3} = 15 - 5(x + 2)
   \]

   On the right-hand side:
   \[
   15 \times \left( - \frac{3(x - 1)}{5} \right) = -3 \times 3(x - 1) = -9(x - 1)
   \]

   So the equation now becomes:
   \[
   15 - 5(x + 2) = -9(x - 1)
   \]

3. **Simplify both sides:**
   
   Expand both sides:

   Left-hand side:
   \[
   15 - 5(x + 2) = 15 - 5x - 10 = 5 - 5x
   \]

   Right-hand side:
   \[
   -9(x - 1) = -9x + 9
   \]

   Now the equation is:
   \[
   5 - 5x = -9x + 9
   \]

4. **Solve for \( x \):**
   
   Collect all terms involving \( x \) on one side and constants on the other side.

   Add \( 9x \) to both sides:
   \[
   5 - 5x + 9x = 9
   \]
   \[
   5 + 4x = 9
   \]

   Subtract 5 from both sides:
   \[
   4x = 4
   \]

   Divide both sides by 4:
   \[
   x = 1
   \]

### Final Answer:
\[
x = 1
\]

---

Do you need further clarification or have any other questions?

Here are 5 related questions to expand on this topic:
1. How would the solution change if there was a different denominator in the equation?
2. What is the process of cross-multiplying to solve equations like this?
3. How can you check your solution to verify that \(x = 1\) is correct?
4. How would the equation change if one of the terms on either side had a different sign?
5. Can this equation be solved graphically by plotting both sides?

**Tip:** Always double-check your solution by substituting the value of \( x \) back into the original equation to verify your work!

Solve the equation 1 - (x + 2)/3 = -(3(x - 1))/5

Learn how to solve the equation 1 - (x + 2)/3 = -(3(x - 1))/5 by finding the least common denominator and using the distributive property. Follow a step-by-step approach suitable for Grades 8-10 students.

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