Question

find the missing number so that the equation has no solutions.
-2x + 7 = \boxed{}x + 12

Explanation:

Step1: Recall no - solution condition

For a linear equation of the form \(ax + b=cx + d\), the equation has no solutions when \(a = c\) and \(b
eq d\). In the given equation \(-2x + 7=\square x+12\), let the missing number be \(m\). So the equation becomes \(-2x + 7=mx + 12\).

Step2: Apply the no - solution condition

We want the coefficients of \(x\) to be equal (so that \(a = c\)) and the constant terms to be different (so that \(b
eq d\)). The coefficient of \(x\) on the left - hand side is \(-2\), and the coefficient of \(x\) on the right - hand side is \(m\). For the equation to have no solutions, we need \(m=-2\) (because when \(m = - 2\), the equation becomes \(-2x+7=-2x + 12\), and if we subtract \(-2x\) from both sides, we get \(7 = 12\), which is a false statement, meaning no solutions exist).

Answer:

\(-2\)