7. The perimeter of a rectangle is 33 inches. - The rectangle has a width of 4 inches. - The rectangle has a length of 2.5 x inches. What is the value of x ? *Must show work*

To find the value of \( x \) in the given rectangle problem, we can follow these steps: 1. **Understand the formula for the perimeter of a rectangle**: The perimeter \( P \) of a rectangle is given by the formula: \[ P = 2 \times (L + W) \] where \( L \) is the length and \( W \) is the width. 2. **Identify the known values**: - The perimeter \( P = 33 \) inches. - The width \( W = 4 \) inches. - The length \( L = 2.5x \) inches. 3. **Substitute the known values into the perimeter formula**: \[ 33 = 2 \times (2.5x + 4) \] 4. **Simplify the equation**: First, divide both sides by 2: \[ 16.5 = 2.5x + 4 \] 5. **Isolate the term with \( x \)**: Subtract 4 from both sides: \[ 16.5 - 4 = 2.5x \] \[ 12.5 = 2.5x \] 6. **Solve for \( x \)**: Divide both sides by 2.5: \[ x = \frac{12.5}{2.5} \] Now, let's calculate the value of \( x \). \[ x = 5 \] Thus, the value of \( x \) is \( 5 \).