https://file.aiquickdraw.com/mathbot/file/1729287260684rw1flcr8.jpg

The equation in the image is:

\[
\frac{p}{17} + \frac{6p}{51} = \frac{1}{3}
\]

Let me solve it step by step.

### Step 1: Simplify the terms
First, simplify the second fraction:
\[
\frac{6p}{51} = \frac{2p}{17} \quad \text{(since } 51 = 17 \times 3)
\]

So the equation becomes:
\[
\frac{p}{17} + \frac{2p}{17} = \frac{1}{3}
\]

### Step 2: Combine like terms
Now, combine the fractions on the left-hand side:
\[
\frac{p + 2p}{17} = \frac{1}{3}
\]

This simplifies to:
\[
\frac{3p}{17} = \frac{1}{3}
\]

### Step 3: Solve for \( p \)
Cross-multiply to eliminate the denominators:
\[
3p \times 3 = 17 \times 1
\]
\[
9p = 17
\]

Now, solve for \( p \) by dividing both sides by 9:
\[
p = \frac{17}{9}
\]

So, the solution is:
\[
p = \frac{17}{9}
\]

Would you like more details on any step, or do you have any questions?

Here are 5 related questions you might explore:
1. How would you check if the solution \( p = \frac{17}{9} \) is correct?
2. Can you generalize the method for solving similar equations with fractions?
3. How would the solution change if the constants in the equation were different?
4. What other methods can be used to solve this kind of equation besides cross-multiplication?
5. How can you interpret this result graphically?

**Tip:** Always check if you can simplify fractions early on to make the equation easier to solve.

Learn how to solve the algebraic equation p/17 + 6p/51 = 1/3 with a detailed step-by-step solution. Simplify fractions, combine like terms, and use cross-multiplication to find p = 17/9. Suitable for students in Grades 8-10.

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