Algebraic equations and solutions from a math worksheet.

Problem Analysis:

The image contains a series of linear equations and their solutions. The task is to solve the given equations step by step and verify the provided solutions.

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Step-by-Step Solution:

#### Equation (i): \( 5x = 25 \)
1. Solve for \( x \):
\[
5x = 25
\]
Divide both sides by 5:
\[
x = \frac{25}{5} = 5
\]

Solution: \( x = 5 \)

---

#### Equation (ii): \( \frac{y}{4} = 20 \)
1. Solve for \( y \):
\[
\frac{y}{4} = 20
\]
Multiply both sides by 4:
\[
y = 20 \times 4 = 80
\]

Solution: \( y = 80 \)

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#### Equation (iii): \( \frac{x}{5} = 2x - 7 \)
1. Eliminate the fraction by multiplying both sides by 5:
\[
x = 10x - 35
\]
2. Rearrange the equation to isolate \( x \):
\[
x - 10x = -35
\]
\[
-9x = -35
\]
3. Solve for \( x \):
\[
x = \frac{-35}{-9} = \frac{35}{9}
\]

Solution: \( x = \frac{35}{9} \)

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#### Equation (iv): \( 3y - 13 = 8 \)
1. Solve for \( y \):
\[
3y - 13 = 8
\]
Add 13 to both sides:
\[
3y = 21
\]
Divide both sides by 3:
\[
y = \frac{21}{3} = 7
\]

Solution: \( y = 7 \)

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#### Equation (v): \( 2(2b + 8) = 256 \)
1. Distribute the 2 on the left-hand side:
\[
4b + 16 = 256
\]
2. Subtract 16 from both sides:
\[
4b = 240
\]
3. Solve for \( b \):
\[
b = \frac{240}{4} = 60
\]

Solution: \( b = 60 \)

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Verification of Provided Solutions:

The solutions provided in the image are listed as follows:
1. \( x = 5 \)
2. \( y = 80 \)
3. \( x = \frac{35}{9} \)
4. \( y = 7 \)
5. \( b = 60 \)

These match the solutions derived above.

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Final Answer:

\[
\boxed{5, 80, \frac{35}{9}, 7, 60}
\]