Given:
[tex](x+2<5)\cup (x-7>-6)[/tex]
To find:
The solution for x.
Solution:
We have,
[tex](x+2<5)\cup (x-7>-6)[/tex] ...(i)
Solve each inequality.
[tex]x+2<5[/tex]
[tex]x<5-2[/tex]
[tex]x<3[/tex]
And,
[tex]x-7>-6[/tex]
[tex]x>-6+7[/tex]
[tex]x>1[/tex]
It means (i) can be rewritten as
[tex](x<3)\cup (x>1)[/tex]
We know that "∪" means solution of x<3 or x>1 both are included in the solution set.
Solution = {x | x<3 or x>1 }
Therefore, the correct option is B.
