Question

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

Answer 1

Answer:

x < 3 and x > -1

Step-by-step explanation:

Step 1: Subtract 2 from both sides.

• $|x-1| + 2 - 2 < 4 - 2$
• $|x-1|$

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.