Let's solve the equation step by step:

Given equation:
\[
-\frac{5}{2}p + \frac{17}{6} = \frac{26}{3}p + \frac{337}{48}
\]

### Step 1: Eliminate the fractions by finding a common denominator
The common denominator for the fractions is 48. Multiply every term in the equation by 48 to eliminate the fractions:

\[
48 \times \left(-\frac{5}{2}p\right) + 48 \times \left(\frac{17}{6}\right) = 48 \times \left(\frac{26}{3}p\right) + 48 \times \left(\frac{337}{48}\right)
\]

This simplifies to:

\[
-120p + 136 = 416p + 337
\]

### Step 2: Move the terms involving \(p\) to one side
Add \(120p\) to both sides to move the \(p\) terms to the right side:

\[
136 = 536p + 337
\]

### Step 3: Isolate the \(p\) term
Subtract 337 from both sides to move the constant terms to the left side:

\[
136 - 337 = 536p
\]

Simplify:

\[
-201 = 536p
\]

### Step 4: Solve for \(p\)
Divide both sides by 536 to isolate \(p\):

\[
p = \frac{-201}{536}
\]

### Step 5: Simplify the fraction (if possible)
The fraction \(\frac{-201}{536}\) is already in its simplest form.

Thus, the solution is:
\[
p = -\frac{201}{536}
\]

Would you like to go over any details or ask further questions?

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Here are five related questions for practice:

1. How would you solve the equation \(\frac{3}{4}p + \frac{1}{8} = \frac{7}{2}p - \frac{5}{16}\)?
2. What is the solution to \(-\frac{7}{3}p + \frac{4}{5} = \frac{14}{9}p + \frac{11}{15}\)?
3. How do you solve an equation where both sides have fractions with different denominators?
4. What is the first step in solving an equation like \(\frac{2}{5}x + \frac{3}{10} = \frac{7}{15}x + \frac{1}{6}\)?
5. How can you check if your solution to a linear equation is correct?

**Tip:** Always start by eliminating fractions in an equation by multiplying through by the least common denominator (LCD) to simplify your work.

Learn how to solve the equation -5/2p + 17/6 = 26/3p + 337/48 with a detailed step-by-step solution. This problem involves equations with fractions and requires arithmetic operations to eliminate fractions and solve for p. Suitable for students in Grades 7-9.

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