The equation given is:

\[
x + 5x + 20x = 100
\]

### Step 1: Combine like terms
On the left-hand side, all the terms involving \( x \) can be combined:

\[
x + 5x + 20x = (1 + 5 + 20)x = 26x
\]

So the equation simplifies to:

\[
26x = 100
\]

### Step 2: Solve for \( x \)
Now, solve for \( x \) by dividing both sides by 26:

\[
x = \frac{100}{26} = \frac{50}{13}
\]

So, \( x = \frac{50}{13} \) or approximately \( 3.846 \).

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Would you like more details or further clarification?

### Related questions:
1. What happens if the equation is changed to \( x + 5x + 20x = 200 \)?
2. How would the solution change if a different term like \( 5x^2 \) was included?
3. How do you solve equations when terms have exponents or higher powers of \( x \)?
4. What are the methods to check the solution for linear equations?
5. Can this equation be solved using graphical methods?

#### Tip:
Always combine like terms first when simplifying equations—this makes the process much faster!

Learn how to solve the linear equation x + 5x + 20x = 100 by combining like terms and simplifying the equation. This problem covers key algebraic concepts such as combining terms and solving for x, suitable for students in Grades 6-8.

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