How many solution$(s)$ of the equation $2x + 1 = x - 3$ are there on the:
$(i)$ Number line
$(ii)$ Cartesian plane

(N/A) $(i)$ The number of solution$(s)$ of the equation $2x + 1 = x - 3$ on the number line is $1$.
Solving the equation: $2x + 1 = x - 3 \Rightarrow 2x - x = -3 - 1 \Rightarrow x = -4$.
Thus,there is exactly one unique solution,$x = -4$,on the number line.
$(ii)$ The number of solution$(s)$ of the equation $2x + 1 = x - 3$ on the Cartesian plane is infinitely many.
In the Cartesian plane,the equation $2x + 1 = x - 3$ can be written as $x + 4 = 0$,which represents a vertical line parallel to the $y$-axis. Every point on this line $( -4, y )$ for any real value of $y$ satisfies the equation,hence there are infinitely many solutions.