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To find the perimeter of each figure, we need to sum the lengths of all the sides.

### a. First figure:
The perimeter \( P \) of the shape is the sum of all its sides. The lengths provided are:

- Top side: \( x \)
- Right side: \( 2x - 4 \)
- Bottom side: \( x + 1 \)
- Left side: \( 2x + 3 \)

So, the perimeter for figure (a) is:

\[
P_a = x + (2x - 4) + (x + 1) + (2x + 3)
\]

Now let's simplify:

\[
P_a = x + 2x - 4 + x + 1 + 2x + 3
\]
\[
P_a = (x + 2x + x + 2x) + (-4 + 1 + 3)
\]
\[
P_a = 6x
\]
\[
P_a = 6x
\]

Thus, the perimeter for figure (a) is \( 6x \).

### b. Second figure:
For the second figure, we sum the following sides:

- Top side: \( x \)
- Right side: \( x \)
- Bottom side: \( x + 2 + x + 3 + x + 4 = 3x + 9 \)
- Left side: \( x \)

The perimeter \( P_b \) is:

\[
P_b = x + x + (3x + 9) + x
\]

Now simplify:

\[
P_b = x + x + 3x + 9 + x
\]
\[
P_b = (x + x + 3x + x) + 9
\]
\[
P_b = 6x + 9
\]

Thus, the perimeter for figure (b) is \( 6x + 9 \).

### Summary of results:
- Perimeter of figure (a): \( 6x \)
- Perimeter of figure (b): \( 6x + 9 \)

Would you like more details on these steps or have any questions?

### Related Questions:
1. What is the perimeter of figure (a) if \( x = 3 \)?
2. How would the perimeters change if we doubled the value of \( x \)?
3. Can you find the area of these figures using the same side lengths?
4. How would the shape change if \( x \) were negative?
5. How could we use the perimeters to solve for \( x \) if the perimeter were given?

### Tip:
When calculating perimeters, make sure to simplify terms as much as possible before substituting values for variables.

Halla el perímetro de cada figura. a. Figura con lados etiquetados como 2x + 3, x + 1, x, 2x - 4. b. Figura con lados etiquetados como x, x + 2, x + 3, x + 4.

This problem involves calculating the perimeter of two composite geometric figures where side lengths are expressed with variables. Learn how to sum algebraic expressions to find the total perimeter in this problem suitable for Grades 8-10.

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