Question

find the missing number so that the equation has no solutions. \boxed{}x - 11 = 4x - 6

Explanation:

Step1: Define the missing coefficient

Let the missing number be $a$. The equation becomes:
$ax - 11 = 4x - 6$

Step2: Rearrange terms to group $x$ terms

Subtract $4x$ from both sides, add 11 to both sides:
$ax - 4x = -6 + 11$
Factor $x$ on the left:
$(a - 4)x = 5$

Step3: Condition for no solution

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 equation becomes $0x=5$, which is false, so no solutions.

Answer:

$4$