Solution: The value of x after solving both components is [tex]2<x\leq11[/tex] or [tex](2,11][/tex].
Explanation:
From the first component it is clearly noticed that the value of x is greater than 2.
Simplify the second component.
[tex]x-1\leq 10\\x\leq 11[/tex]
From the above inequality it is clearly noticed that the value of x is less than or equal to 11.
Solving both components we get [tex]2<x\leq11[/tex] and the graphical representation is shown in the figure.
The red portion shows the solutions of [tex]x>2[/tex], blue portion shows the solution of [tex]x-1\leq 10[/tex] and purple portion which combination of red and blue portion shows the solution of both inequalities.
Therefore, value of x after solving both components is [tex]2<x\leq11[/tex] or [tex](2,11][/tex].
