Question

find the missing number so that the equation has no solutions. \boxed{}x - 7 = -2x - 19

Explanation:

Step1: Let missing value be $a$

Let the blank be $a$, so the equation becomes:
$ax - 7 = -2x - 19$

Step2: Rearrange like terms

Bring all $x$-terms to left, constants to right:
$ax + 2x = -19 + 7$
Factor $x$ on the left:
$(a + 2)x = -12$

Step3: Set for no solution

For no solution, the coefficient of $x$ must be 0, while the constant term is non-zero.
Set $a + 2 = 0$
$a = -2$
Verify: When $a=-2$, left side is $0x=0$, right side is $-12$, so $0=-12$ which is false, no solution.

Answer:

$-2$