How many solutions exist for the given equation? 3(x + 10) + 6 = 3(x + 12) Options: zero, one, two, infinitely many

To determine how many solutions exist for the equation 3 ( x + 10 ) + 6 = 3 ( x + 12 ) , let's simplify both sides and compare them.
First, distribute the 3 on both sides:

Left side: 3 ( x + 10 ) + 6 = 3 x + 30 + 6 = 3 x + 36

Right side: 3 ( x + 12 ) = 3 x + 36


Now, both sides of the equation are:
3 x + 36 = 3 x + 36
Since these expressions are identical after simplification, it means that the equation is true for any value of x . This means that there are infinitely many solutions.
Thus, the answer to the multiple-choice question is: infinitely many.

Answered by danjohnbrain | 2025-07-22