Find the Intersection x+1>3 , x-2>4

$x + 1 > 3$ , $x - 2 > 4$

Move all terms not containing $x$ to the right side of the inequality.

Subtract $1$ from both sides of the inequality.

$x > 3 - 1$ and $x - 2 > 4$

Subtract $1$ from $3$ .

$x > 2$ and $x - 2 > 4$

Move all terms not containing $x$ to the right side of the inequality.

Add $2$ to both sides of the inequality.

$x > 2$ and $x > 4 + 2$

Add $4$ and $2$ .

$x > 2$ and $x > 6$

The intersection consists of the elements that are contained in both intervals.

$x > 6$

The result can be shown in multiple forms.

Inequality Form:

$x > 6$

Interval Notation:

$(6, \infty)$