Starting claim: 2x + 5 > 9 or x + 1 < 0
2x + 5 - 5 > 9 - 5 or x + 1 - 1 < 0 - 1
2x > 4 or x < -1
Finally, divide both sides by (+2) on the left:
x > 2 or x < -1

x < -1 or x > 2

Notice that it is impossible for both x < -1 AND x > 2
to be true about the same number x.