Solve absolute value of (x+1) more or equal to 3?

Answer 1

| x + 1 | ≥ 3
x + 1 ≥ 3
x ≥ 2
OR
x + 1 ≤ - 3
x ≤ - 4

Answer 2

Hi,
It appears that your problem is this:
|x +1| ≥ 3
So, the term inside the absolute value sign can be -3 or 3. So, for the negative to be greater than 3, the term inside must be <-3. So, we write this:
x+1 > 3
x > 2 (Subtract 1 from each side.)

Then, x+1 < -3
X < -4
So, our answer is that x < -4 and x> 2
Writing this in interval notation we have:
(-oo, -4] U [2, oo) Where I’ve used oo for infinity.

Hope this helps.
FE

Answer 3

|x + 1| >= 3
x + 1 >= 3 or x + 1 <= -3
x >= 2 or x <= -4

Answer 4

|x+1|≥3 <--> x+1≤-3 or x+1≥3 <--> x≤-4 or x≥2 <-->

S= {x in (-inf, -4] U [2, +inf)}

Saludos.