`(2x+7)/5 - (3x+11)/2 = (2x+8)/3 -5`

Options

A. 1
B. -1
C. 2
D. -2

Answer

To solve the equation \((2x + 7)/5 - (3x + 11)/2 = (2x + 8)/3 - 5\), we will follow these steps:

### Step 1: Find a common denominator
The denominators in the equation are 5, 2, and 3. The least common multiple (LCM) of these numbers is 30. We will multiply each term by 30 to eliminate the fractions.

\[ 30 \left(\frac{2x + 7}{5}\right) - 30 \left(\frac{3x + 11}{2}\right) = 30 \left(\frac{2x + 8}{3}\right) - 30(5) \]

### Step 2: Simplify each term
Now we simplify each term:

\[ 6(2x + 7) - 15(3x + 11) = 10(2x + 8) - 150 \]

### Step 3: Distribute
Distributing the terms gives us:

\[ 12x + 42 - 45x - 165 = 20x + 80 - 150 \]

### Step 4: Combine like terms
Now, we combine like terms on both sides:

Left side:
\[ 12x - 45x + 42 - 165 = -33x - 123 \]

Right side:
\[ 20x + 80 - 150 = 20x - 70 \]

So we have:
\[ -33x - 123 = 20x - 70 \]

### Step 5: Move all x terms to one side
Now, we will move all \(x\) terms to the left side and constant terms to the right side:

\[ -33x - 20x = -70 + 123 \]

### Step 6: Combine like terms again
This simplifies to:

\[ -53x = 53 \]

### Step 7: Solve for x
Now, divide both sides by -53:

\[ x = -1 \]

### Final Answer
Thus, the solution to the equation is:

\[ \boxed{-1} \]

---