Step by step
The question
Question: solve x + 1 < 4 or x + 1 > 2.
Two inequalities, joined by "or".
x + 1 < 4 or x + 1 > 2
"Or" means: x can make one of them true, or the other.
We solve both, side by side.
or: one of them is true
1 Remove the + 1
We want x by itself.
The + 1 is in the way.
In each one, we take away 1 on both sides.
x + 1 − 1 < 4 − 1 or x + 1 − 1 > 2 − 1
+ 1 and − 1 make zero, in both.
4 minus 1 is 3.
2 minus 1 is 1.
4 − 1 = 3, 2 − 1 = 1
So x < 3 or x > 1.
x < 3 or x > 1
Every number is less than 3 or more than 1.
So every number works.
Every number is in one of the parts.
Answer
x < 3 or x > 1