Question

find the missing number so that the equation has no solutions. \square x - 17 = -4x - 7

Explanation:

Step1: Let missing value be $a$

Let the unknown coefficient be $a$, so the equation becomes:
$ax - 17 = -4x - 7$

Step2: Rearrange like terms

Bring all $x$-terms to the left and constants to the right:
$ax + 4x = 17 - 7$
Factor out $x$:
$(a + 4)x = 10$

Step3: Set for no solutions

A linear equation $mx = n$ has no solutions if $m=0$ and $n
eq0$. Set $a + 4 = 0$:
$a + 4 = 0 \implies a = -4$
Verify: When $a=-4$, the left side is $0x=0$, right side is $10$, so $0=10$ which is false, no solutions.

Answer:

$-4$