The intersection of [tex](x+1<5) \cap(x-4>-3)[/tex] is [tex](1,4)[/tex]
Explanation:
The expression is [tex](x+1<5) \cap(x-4>-3)[/tex]
To determine the intersection of these two inequalities, let us solve the two inequalities separately.
Consider [tex]x+1<5[/tex]
Subtracting both sides by 1, we have,
[tex]x<4[/tex]
Also, consider [tex]x-4>-3[/tex]
Adding both sides by 4, we have,
[tex]x>1[/tex]
Using these two simplified inequalities in the expression, we have,
[tex](x<4) \cap(x>1)[/tex]
Writing this in the interval notation, we get,
[tex](-\infty, 4) \cap(1, \infty)[/tex]
Hence, the intersection of the two interval is
[tex](1,4)[/tex]
Thus, the intersection of [tex](x+1<5) \cap(x-4>-3)[/tex] is [tex](1,4)[/tex]
