4x+3 ≤ |1-3x| Help?

Case I : When x ≥ 1/3, i.e. (1 - 3x) ≤ 0 and |1 - 3x| = -(1 - 3x)
4x + 3 ≤ -(1 - 3x) and x ≥ 1/3
4x + 3 ≤ -1 + 3x and x ≥ 1/3
x ≤ -4 and x ≥ 1/3
There is no solution in Case I.

Case II : When x < 1/3, i.e. (1 - 3x) > 0 and |1 - 3x| = 1 - 3x
4x + 3 ≤ 1 - 3x and x < 1/3
7x ≤ -2 and x < 1/3
x ≤ -2/7 and x < 1/3
Range of x in Case II: x ≤ -2/7

Refer to Case I and Case II.
Range of x: x ≤ -2/7

Case 1: 1-3x >= 0

|1-3x| = 4x+3
1-3x >= 4x+3

1-3x >=4x+3
1-7x >=3
-7x >= 2
-x >=2/7
x <= -2/7

Case 2:
1-3x <=0
-3x <= -1
x >= 1/3
|1-3x| = 3x-1
3x-1 >= 4x+3
4x+3 <= 3x-1
x+ 3 <= -1
x <= -4
x <= -4 and x >= 1/3 (not possible)

x <= -2/7