What number gives the same result when it is added to five as when it is multiplied by 5

Let's denote the unknown number as \( x \).

The problem states that the number gives the same result when it is added to 5 as when it is multiplied by 5. This can be expressed algebraically as:

\[
x + 5 = 5x
\]

Now, solve for \( x \):

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

2. Simplify the right-hand side:
\[
5 = 4x
\]

3. Divide both sides by 4:
\[
x = \frac{5}{4}
\]

So, the number is \( \frac{5}{4} \) or 1.25.

Would you like further explanation or have any questions on this?

Here are 5 related questions to explore this topic further:
1. How can we verify the solution \( x = 1.25 \)?
2. What other types of equations can be solved using similar techniques?
3. Can this type of equation have more than one solution?
4. What happens if we change the problem to involve subtraction or division?
5. How would this equation change if we included variables on both sides?

**Tip**: When solving equations, isolate the variable on one side by performing inverse operations (like adding, subtracting, or dividing).

What number gives the same result when it is added to five as when it is multiplied by 5?

Discover how to solve a linear equation where a number added to 5 gives the same result as when it is multiplied by 5. This step-by-step solution covers key algebra concepts for students in Grades 6-8.

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