Question

how many solutions exist for the given equation?
$12x + 1 = 3(4x + 1) - 2$
options: one, infinitely many, zero, (another option with text not?)

Explanation:

Step1: Expand the right side

First, expand \( 3(4x + 1)-2 \). Using the distributive property, \( 3(4x + 1)=12x + 3 \), so the right side becomes \( 12x + 3 - 2=12x + 1 \).

Step2: Compare both sides

Now the equation is \( 12x + 1 = 12x + 1 \). Subtract \( 12x \) from both sides, we get \( 1 = 1 \), which is always true. This means the equation is an identity, so there are infinitely many solutions.

Answer:

infinitely many