https://file.aiquickdraw.com/mathbot/file/172620639186210f8tpaq.jpg

The equation in the image is:

\[
\frac{1}{6}p = \frac{1}{5}p + \frac{2}{3}
\]

### Steps to solve:

1. **Eliminate the fractions** by finding a common denominator. The denominators are 6, 5, and 3. The least common denominator (LCD) of 6, 5, and 3 is 30.
   
   Multiply both sides of the equation by 30 to clear the fractions:

   \[
   30 \cdot \left(\frac{1}{6}p\right) = 30 \cdot \left(\frac{1}{5}p + \frac{2}{3}\right)
   \]

   Simplifying:

   \[
   5p = 6p + 20
   \]

2. **Simplify the equation** by subtracting \(6p\) from both sides:

   \[
   5p - 6p = 20
   \]

   \[
   -p = 20
   \]

3. **Solve for \(p\)** by multiplying both sides by \(-1\):

   \[
   p = -20
   \]

### Final Solution:

\[
p = -20
\]

Would you like further details on any part of the solution or have any questions?

---

Here are 5 related questions you might want to explore:

1. How do you solve linear equations involving fractions?
2. What is the significance of the least common denominator (LCD) when solving equations?
3. Can the value of \(p\) be checked by substituting it back into the original equation?
4. How can you handle equations with multiple variables?
5. What happens if both sides of an equation contain more complex expressions?

**Tip:** Always aim to eliminate fractions early in solving equations, as this simplifies the overall process and reduces calculation errors.

Learn how to solve the linear equation involving fractions: 1/6p = 1/5p + 2/3. This detailed step-by-step solution simplifies the equation by eliminating fractions and solving for p. Suitable for Grades 8-10.

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