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Let's solve these questions step-by-step.

### Question 26:
To find the perimeter of the given shape, we need to add up all the side lengths. The shape has four labeled sides:
- Two sides with length \((x + 1)\) cm.
- Two sides with length \((2x - 3)\) cm.

The perimeter \(P\) is given by:
\[
P = 2(x + 1) + 2(2x - 3)
\]

Expanding each term:
\[
P = 2x + 2 + 4x - 6
\]

Combining like terms:
\[
P = 6x - 4
\]

So, the expression for the perimeter is:
**\(6x - 4\) cm**.

However, this answer isn't an option. This could be an error in the answer options or in interpreting the question. Let's move to question 27 based on this answer for perimeter.

### Question 27:
Given that the perimeter is 46 cm, we can set up the equation:
\[
6x - 4 = 46
\]

Adding 4 to both sides:
\[
6x = 50
\]

Dividing by 6:
\[
x = \frac{50}{6} = 8.33 \, (\text{approximately})
\]

Since this value does not exactly match any of the provided answers, the closest choice would be to check if there's an alternative approach or error in the answer options given. 

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Let me know if you'd like further assistance on interpreting the problem, or if there's more context to review for adjustments. 

### Relative Questions:
1. How would you calculate perimeter if additional sides were labeled?
2. Why might the provided answer choices differ from calculated results?
3. How would solving perimeter differ for different polygons?
4. How to verify solutions when answer options seem inconsistent?
5. What approach helps in confirming polynomial simplifications?

### Tip:
Always recheck given answer choices against your calculations for accuracy; sometimes answers contain rounding or estimation.

For questions 26-27, refer to the following information.

26. Find an expression for the perimeter of the figure with side lengths (x + 1) cm and (2x - 3) cm.
27. If the perimeter is equal to 46 cm, find x.

Solve for the perimeter expression of a quadrilateral with side lengths (x + 1) cm and (2x - 3) cm, and find the value of x when the perimeter is 46 cm. This problem involves algebraic concepts and linear equations suitable for students in Grades 8-10.

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