Question

Which of these equations has an infinite number of solutions? In other words, if you substitute any value for x, which equation will always be true?

x−2=8

x−5=x−5

4x=12

Answer 1

To determine which equation has an infinite number of solutions, we can analyze each equation:

1. **\(x - 2 = 8\)**
- To solve for \(x\), we add 2 to both sides:
\(x = 8 + 2\)
\(x = 10\)
- This equation has a **unique solution**: \(x = 10\).

2. **\(x - 5 = x - 5\)**
- In this equation, both sides are identical, meaning this equation is always true regardless of the value of \(x\).
- Therefore, this equation has **an infinite number of solutions**.

3. **\(4x = 12\)**
- To solve for \(x\), we divide both sides by 4:
\(x = \frac{12}{4}\)
\(x = 3\)
- This equation has a **unique solution**: \(x = 3\).

Among the equations provided, **\(x - 5 = x - 5\)** is the one that has an infinite number of solutions.