Question

find the missing number so that the equation has no solutions. \boxed{}x + 10 = -2(x - 16)

Explanation:

Step1: Let missing value be $a$

Let the missing number be $a$, so the equation becomes:
$ax + 10 = -2(x - 16)$

Step2: Expand right-hand side

Distribute $-2$ on the right:
$ax + 10 = -2x + 32$

Step3: Rearrange like terms

Bring all $x$ terms to left, constants to right:
$ax + 2x = 32 - 10$
$(a + 2)x = 22$

Step4: Set coefficient of $x$ to 0

For no solution, the coefficient of $x$ must be 0 (so $0x = 22$, which is false):
$a + 2 = 0$
$a = -2$

Answer:

$-2$