Question

find the missing number so that the equation has infinitely many solutions.
$-3x + \square - x = -4x + 12$

Explanation:

Step1: Combine like terms on the left

Combine the \(x\)-terms: \(-3x - x = -4x\), so the left side becomes \(-4x + \square\).

Step2: Analyze infinite solutions condition

For an equation \(ax + b = cx + d\) to have infinitely many solutions, we need \(a = c\) and \(b = d\). Here, the left side is \(-4x + \square\) and the right side is \(-4x + 12\). So we need \(\square = 12\) to satisfy \(b = d\) (since \(a = c = -4\) already holds).

Answer:

12