Xavier Aptitude Test 2023 Paper

Given equation, $\mathit{A}=|\mathit{x}+3|+|\mathit{x}-2|-|2\mathit{x}-8|$.
Case (i):-
then, $\mathit{A}=\mathit{x}+3+\mathit{x}-2-2\mathit{x}+8=9$.
The maximum value of $\left|\mathrm{A}\right|=9$
Case (ii):-

then $\mathit{A}=\mathit{x}+3+\mathit{x}-2+2\mathit{x}-8=4\mathit{x}-7$
The range of $\mathit{x}$ is $\left[2,4\right)$. Hence the value of $\mathit{A}$ varies from $\left[1,9\right)$.
The maximum value of

Case (iii):

then $\mathit{A}=\mathit{x}+3-\mathit{x}+2+2\mathit{x}-8=2\mathit{x}-3$.
The range of $\mathit{x}$ is $\left[-3,2\right)$. Hence the value of $\mathit{A}$ varies from $\left[-9,1\right)$.
The maximum value of $\left|\mathit{A}\right|=9$
Case (iv):

then $\mathit{A}=-\mathit{x}-3-\mathit{x}+2+2\mathit{x}-8=-9$.
The maximum value of $\left|\mathit{A}\right|=9$
From the above cases, The maximum value of $\left|\mathit{A}\right|=9$. Option (B) is correct.