To find the width of the rectangle, we start with the formula for the perimeter of a rectangle:

$\text{Perimeter} = 2(\text{Length} + \text{Width})$

Given:

• Perimeter $= 10x + 6$
• Length $= 3x - 3$

Step 1: Substitute the values into the formula

$10x + 6 = 2\left((3x - 3) + \text{Width}\right)$

Step 2: Simplify the equation

$10x + 6 = 2(3x - 3 + \text{Width})$ Distribute the $2$: $10x + 6 = 6x - 6 + 2\text{Width}$

Step 3: Isolate $2\text{Width}$

$10x + 6 - 6x + 6 = 2\text{Width}$ $4x + 12 = 2\text{Width}$

Step 4: Solve for $\text{Width}$

$\text{Width} = \frac{4x + 12}{2}$ $\text{Width} = 2x + 6$

Final Answer:

The width of the rectangle is: $\boxed{2x + 6}$

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Here are some related questions to deepen your understanding:

1. What would the width be if $x = 2$?
2. How would the formula change if the perimeter were doubled?
3. What is the area of the rectangle in terms of $x$?
4. What happens to the width if the length is halved?
5. How do you solve for $x$ if you are given the width?

Tip: Always double-check your calculations when substituting variables into formulas.