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?

Question

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.