Question

find the missing number so that the equation has no solutions.
-4x - 14 = \square x + 4

Explanation:

Step1: Define missing coefficient

Let the missing number be $a$. The equation becomes:
$$-4x -14 = ax +4$$

Step2: Rearrange like terms

Move all $x$ terms to left and constants to right:
$$-4x -ax = 4 +14$$
$$(-4-a)x = 18$$

Step3: Force no solution

A linear equation $mx = b$ has no solutions if $m=0$ and $b
eq0$. Set $-4-a=0$:
$$-4-a=0 \implies a=-4$$
Verify: $0x=18$, which is always false.

Answer:

$\boldsymbol{-4}$