1. It should have been:
x – 5 > 12
Add 12 on both sides of the inequality:
x – 5 + 5 > 12 + 5
x > 1
2. 3 < x + 2
Switch sides:
x + 2 < 3
Subtract 2 on both sides of the inequality to isolate x:
x + 2 – 2 < 3 – 2
x < 1
Please see the attached image for the graphing of the solutions on the number line.