Answer:
x < 3 and x > -1
Step-by-step explanation:
Step 1: Subtract 2 from both sides.
- [tex]|x-1| + 2 - 2 < 4 - 2[/tex]
- [tex]|x-1|<2[/tex]
Step 2: Solve absolute value.
- We know x - 1 < 2 and x - 1 > -2.
Condition 1:
- [tex]x - 1 < 2[/tex]
- [tex]x - 1 + 1 < 2 + 1[/tex] (Add 1 to both sides)
- [tex]x < 3[/tex]
Condition 2:
- [tex]x - 1 > -2[/tex]
- [tex]x - 1 + 1 > -2 + 1[/tex] (Add 1 to both sides)
- [tex]x>-1[/tex]
Therefore, the answer is x < 3 and x > -1.
