Solve the Inequality for x -3<x+2<7

$- 3 < x + 2 < 7$

Subtract $2$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 3 - 2 < x < 7 - 2$

Subtract $2$ from $- 3$ .

$- 5 < x < 7 - 2$

Subtract $2$ from $7$ .

$- 5 < x < 5$

The result can be shown in multiple forms.

Inequality Form:

$- 5 < x < 5$

Interval Notation:

$(- 5, 5)$