Find the value of p from `2/x+p=3`, when `(5(7x+5))/3-23/3=13-((4x-2)/3)`

Options

A. 0
B. 1
C. 2
D. 3

Answer

To solve the equation and find the value of \( p \) from the equation \( \frac{2}{x} + p = 3 \) when \( \frac{5(7x + 5)}{3} - \frac{23}{3} = 13 - \frac{4x - 2}{3} \), we will follow these steps:

### Step 1: Simplify the equation
We start with the equation:
\[ \frac{5(7x + 5)}{3} - \frac{23}{3} = 13 - \frac{4x - 2}{3} \]

### Step 2: Combine like terms on the left side
Multiply out the left side:
\[ \frac{35x + 25}{3} - \frac{23}{3} = \frac{35x + 25 - 23}{3} = \frac{35x + 2}{3} \]

### Step 3: Simplify the right side
For the right side, we can express 13 with a common denominator of 3:
\[ 13 = \frac{39}{3} \]
Thus, the right side becomes:
\[ \frac{39}{3} - \frac{4x - 2}{3} = \frac{39 - (4x - 2)}{3} = \frac{39 - 4x + 2}{3} = \frac{41 - 4x}{3} \]

### Step 4: Set the two sides equal
Now we have:
\[ \frac{35x + 2}{3} = \frac{41 - 4x}{3} \]

### Step 5: Eliminate the denominators
Multiply both sides by 3 to eliminate the fractions:
\[ 35x + 2 = 41 - 4x \]

### Step 6: Solve for \( x \)
Add \( 4x \) to both sides:
\[ 35x + 4x + 2 = 41 \]
\[ 39x + 2 = 41 \]
Subtract 2 from both sides:
\[ 39x = 39 \]
Divide by 39:
\[ x = 1 \]

### Step 7: Substitute \( x \) back to find \( p \)
Now substitute \( x = 1 \) back into the equation \( \frac{2}{x} + p = 3 \):
\[ \frac{2}{1} + p = 3 \]
This simplifies to:
\[ 2 + p = 3 \]
Subtract 2 from both sides:
\[ p = 3 - 2 \]
\[ p = 1 \]

### Final Answer
The value of \( p \) is \( 1 \).

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