When eight times a number is increased by five, the result is equal to the original number plus twenty-six.

Let's break down the problem and solve for the unknown number.

### Step 1: Set up the equation
Let the unknown number be denoted by \( x \).

According to the problem:
- "Eight times a number" is represented as \( 8x \).
- "Increased by five" means adding 5 to \( 8x \), giving us \( 8x + 5 \).
- This is "equal to the original number plus twenty-six," which is represented as \( x + 26 \).

So, the equation is:
\[
8x + 5 = x + 26
\]

### Step 2: Solve the equation
To solve for \( x \), first, let's get all terms involving \( x \) on one side and the constant terms on the other side.

1. Subtract \( x \) from both sides:
\[
8x - x + 5 = 26
\]
\[
7x + 5 = 26
\]

2. Subtract 5 from both sides:
\[
7x = 21
\]

3. Finally, divide both sides by 7 to solve for \( x \):
\[
x = 3
\]

### Step 3: Verification
Let's verify the solution by substituting \( x = 3 \) back into the original problem.

- Eight times the number: \( 8 \times 3 = 24 \).
- Increased by five: \( 24 + 5 = 29 \).
- The original number plus twenty-six: \( 3 + 26 = 29 \).

Both sides are equal, so our solution \( x = 3 \) is correct.

### Final Answer:
The number is \( 3 \).

Would you like more details or have any questions?

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Here are 8 related questions for further practice:

1. What is the solution for \( 5x + 7 = 3x + 21 \)?
2. Solve for \( x \): \( 9x + 4 = 2x + 18 \).
3. If six times a number is reduced by 11, the result is equal to twice the original number plus 13. Find the number.
4. Solve the equation: \( 4(x + 2) = 2x + 14 \).
5. What is the value of \( x \) in \( 10x - 15 = 3x + 12 \)?
6. If three times a number is increased by 10, the result is equal to twice the original number plus 15. Find the number.
7. Solve for \( x \): \( 7(x - 3) + 2 = 5x + 10 \).
8. What is the solution for \( 6x + 8 = 4x + 20 \)?

**Tip:** Always double-check your solution by substituting it back into the original equation to verify correctness.

Learn how to solve the equation 8 times a number increased by 5 equals the original number plus 26 with a step-by-step solution. This problem involves linear equations and is suitable for students in Grades 7-9.

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