Question

how many solutions exist for the givien equation 3(x+10)+6=3(x+12)​

Answer 1

For this case we solve the following equation:

$3 (x + 10) + 6 = 3 (x + 12)$

We apply distributive property to the terms within parentheses:

$3x + 30 + 6 = 3x + 36$

We add similar terms:

$3x + 36 = 3x + 36\\36 = 36$

Since 36 equals 36, then the equation will always be true for any value of x.

ANswer:

Infinite solutions