Question

complete the equation so it has infinitely many solutions.
12y + 3 = 10y + 2y + \square

Explanation:

Step1: Combine like terms on RHS

First, simplify \(10y + 2y\) on the right - hand side (RHS) of the equation. According to the rule of combining like terms (terms with the same variable), \(10y+2y=(10 + 2)y=12y\). So the equation becomes \(12y + 3=12y+\square\).

Step2: Determine the value for infinitely many solutions

For an equation of the form \(ax + b=ax + c\) to have infinitely many solutions, the constant terms \(b\) and \(c\) must be equal. In our equation, \(a = 12\), \(b = 3\), and we need to find \(c\) (the value in the square) such that \(12y+3 = 12y + c\). Subtracting \(12y\) from both sides of the equation, we get \(3=c\). So the value in the square should be 3.

Answer:

3