Which graph represents the solution of |–2 + (x – 3)| < 7?

D

Step-by-step explanation:

the "<" (or "smaller") symbol tells us that the solution must have empty dots at the interval ends, as these values are not included in the solution.

otherwise, we would have a "<=" ("smaller or equal") symbol.

let's start for the first limit to calculate without the absolute value :

-2 + (x - 3) < 7

-5 + x < 7

x < 12

the other end we get by multiplying only the left side (still without the absolute value) by -1 and do it again :

-1×(-2 + (x - 3)) < 7

2 - (x - 3) < 7

2 - x + 3 < 7

-x + 5 < 7

-x < 2

x > -2 (remember, when we multiply the whole inequality, left and right side, by a negative value, we need to flip the inequality symbol).