how many solutions exist for the given equation? 3(x + 10) + 6 = 3(x + 12)\nzero\none\ntwo\ninfinitely many

Explanation:

Step1: Expand both sides

$3(x + 10)+6=3x+30 + 6=3x + 36$ and $3(x + 12)=3x+36$.

Step2: Simplify the equation

The original equation $3(x + 10)+6 = 3(x + 12)$ becomes $3x+36=3x + 36$.

Step3: Analyze the result

Subtracting $3x$ from both sides gives $36=36$, which is always true regardless of the value of $x$.

Answer:

infinitely many