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Solve for perimeter by adding up all the sides and solve for x

To find the perimeter of this rectangle, we will sum up all the sides.

From the image:
- One pair of opposite sides is labeled as \(5x - 15\) and \(2x - 3\),
- The other pair is labeled as \(x - 1\) (opposite sides of a rectangle are equal).

### Step 1: Express the perimeter

The perimeter \(P\) of a rectangle is calculated by adding all sides or using the formula:

\[
P = 2(\text{length} + \text{width})
\]

From the image, the lengths and widths are:

- Two lengths: \(5x - 15\) and \(2x - 3\)
- Two widths: \(x - 1\) (repeated on both sides)

Thus, the perimeter is:

\[
P = 2\left((5x - 15) + (x - 1)\right)
\]

### Step 2: Simplify the expression for the perimeter

First, combine the terms inside the parentheses:

\[
P = 2\left((5x - 15) + (x - 1)\right)
\]
\[
P = 2\left(5x + x - 15 - 1\right)
\]
\[
P = 2\left(6x - 16\right)
\]

Now, distribute the 2:

\[
P = 12x - 32
\]

### Step 3: Solve for \(x\)

If there is a specific value for the perimeter provided (such as a numerical value), we could solve for \(x\). However, the image does not specify a perimeter value. If you have this value, you can set the equation equal to that number and solve for \(x\).

Would you like to provide a specific perimeter or clarify any other details?

### Related Questions:
1. How would the equation change if the rectangle was a square?
2. What happens to the perimeter when \(x\) is a negative number?
3. Can you solve for \(x\) if the area of the rectangle is given?
4. How does the perimeter change as \(x\) increases?
5. What is the difference between finding the perimeter and finding the area in this case?

### Tip:
When solving for variables in expressions involving perimeter or area, always combine like terms carefully before substituting or simplifying further.

Learn how to solve for x in a rectangle perimeter problem with variables. Using the perimeter formula for rectangles and simplifying algebraic expressions, this problem is suitable for students in Grades 7-9. It covers key concepts in geometry and algebra.

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