Question

6x + 12 = 2(3x + 6).

Can you find the number of solutions this equation has without solving for x? Pls explain.

Answer 1

infinite number of solutions

Explanation:

If you just distribute the 2 on the right side of the equation,

6x + 12 = 2(3x + 6)

6x + 12 = 6x + 12

The two sides of the equation are identical. And if we were to proceed to solve (but they said don't) and subtracted 6x from both sides we would get 12 = 12 .

The variable falls out of the equation and a true statement is left behind, there are infinite solutions.