Answer
$\color{blue}{\bf\text{A, B }}$
Work Step by Step
Remember, we are asked to find the $\bf{incorrect}$ options.
If $x$ is the number of pennies in a jar, which are physical objects, then
$\bf{x}$ is a $\bf\text{whole number}$,
because you can't cut a coin in pieces or have a negative number of physical objects.
So, we can solve each equation and see if the solution meets our criteria:
Consider $\bf\text{option A}$ : $5x+3=11$
$5x=8$
$x=\dfrac{8}{5}$
We can't have a fraction of a coin so $\bf\text{option A is incorrect}$
Consider $\bf\text{option B}$ : $12x+6=-4$
$12x=-10$
$x=-5/6$
We can't have a fraction of a coin so $\bf\text{option B is incorrect}$
Consider $\bf\text{option C}$ : $100x=50(x+3)$
$100x=50x+150$
$50x=150$
$x=3$
Since $3$ is a valid number of pennies $\bf\text{option C is correct}$
Consider $\bf\text{option D}$ : $6(x+4)=x+24$
$6x+24=x+24$
$5x=0$
$x=0$
Since $0$ is a valid number of pennies in an empty jar, $\bf\text{option D is correct}$
Therefore, the $\bf\text{incorrect}$ options are $\color{blue}{\bf\text{A & B}}$
