Question

Write an equation with a variable on both sides of the equal sign that has infinitely many solutions. Solve the equation and explain why it has an infinite number of solutions.

Answer 1

One example is the equation:

2x + 6 = 4x/2 + 12/2

To solve this, we need to transpose like terms to the same side.

2x - 4x/2 = 12/2 - 6
2x - 2x = 6 - 6
0 = 0

Since both sides are zero, it means that the equation has infinite number of solutions.