If the perimeter of a triangle is `8x -7` and two sides are `3x +5` and `2x - 3`, find the third side.

Options

A. 7x - 9
B. 3x - 6
C. 6x -7
D. 3x - 9

Answer

To find the third side of the triangle given the perimeter and two sides, we can follow these steps:

### Step 1: Write down the information given
The perimeter of the triangle is given as \(8x - 7\). The two sides of the triangle are \(3x + 5\) and \(2x - 3\).

### Step 2: Set up the equation for the perimeter
The perimeter of a triangle is the sum of all its sides. We can express this as:
\[ \text{Perimeter} = \text{Side 1} + \text{Side 2} + \text{Side 3} \]
Let the third side be \(z\). Therefore, we can write:
\[ 8x - 7 = (3x + 5) + (2x - 3) + z \]

### Step 3: Simplify the equation
Combine the two sides:
\[ 8x - 7 = 3x + 5 + 2x - 3 + z \]
Combine like terms:
\[ 8x - 7 = (3x + 2x) + (5 - 3) + z \]
This simplifies to:
\[ 8x - 7 = 5x + 2 + z \]

### Step 4: Isolate \(z\)
To find \(z\), we need to isolate it on one side of the equation. We can do this by subtracting \(5x + 2\) from both sides:
\[ z = (8x - 7) - (5x + 2) \]

### Step 5: Simplify the expression for \(z\)
Now, simplify the right-hand side:
\[ z = 8x - 7 - 5x - 2 \]
Combine like terms:
\[ z = (8x - 5x) + (-7 - 2) \]
This results in:
\[ z = 3x - 9 \]

### Conclusion
The third side of the triangle is:
\[ \boxed{3x - 9} \]