Solution :
We have to find all the possible solutions for the inequality [tex]2x+7<3x-5[/tex].
The given inequality can be solved as,
Subtracting 7 from both side , we get
[tex]2x+7-7 < 3x-5-7\\\\\Rightarrow 2x<3x-12[/tex]
Now, Subtracting 3x from both side, we get
[tex]2x-3x<3x-12-3x\\\Rightarrow -x <-12\\[/tex]
As we here we can see that both sides have similar sign, so we can cancel them out.
[tex]\Rightarrow x < 12[/tex]
Hence, the possible solution of the inequality [tex]2x+7<3x-5[/tex] is [tex]x< 12[/tex]
