For what integer value of X is 3x+5> 11 and x-3 <1?
The information given just offered upper and lower bounds for x,
but you have to rewrite them.
$\displaystyle 3x+5>11\Rightarrow\ 3x+5>6+5\Rightarrow\ 3x>6\Rightarrow\ 3x>3(2)\Rightarrow\ x>2$
$\displaystyle x-3<1\Rightarrow\ x-3<4-3\Rightarrow\ x<4$
Then the allowable integer value(s) of x is much clearer.