Question

|x-1|+2<4 solving for x

Answer 1

x < 3 and x > -1

Explanation:

Step 1: Subtract 2 from both sides.

• 
  `|x-1| + 2 - 2 < 4 - 2`
• 
  `|x-1|<2`

Step 2: Solve absolute value.

• We know x - 1 < 2 and x - 1 > -2.

Condition 1:

• 
  `x - 1 < 2`
• 
  `x - 1 + 1 < 2 + 1` (Add 1 to both sides)
• 
  `x < 3`

Condition 2:

• 
  `x - 1 > -2`
• 
  `x - 1 + 1 > -2 + 1` (Add 1 to both sides)
• 
  `x>-1`

Therefore, the answer is x < 3 and x > -1.