Solve |x+1|>4,xϵR
We have, |x+1|>a⇔x<−a or x>a
∴ |x+1|>4⇔x+1<−4 or x+1>4
⇔x<−4−1 or x>4−1
⇔ x<−5 or x>3
⇔xϵ(−∞,−5) or xϵ(3,∞)
∴ solution set =(−∞,−5)∪(3,∞)
Solve
|x−1|+|x−2|≥4,xϵR
Solve the following system of equations in R.
4x+1≤3≤6x+1,x>0