How do you graph and solve # |3 - 2x| ≥ 4#?

Question

5342 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-19T04:14:15

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

Separate solving in 2 parts:
a. #(3 - 2x) >= 4#
#- 2x >+ 1#
#2x <= -1/2# --> #x <= - 1/4#
b. -(3 - 2x) >= 4
-3 + 2x >= 4
2x >= 7 --> #x >= 7/2#

Solution set: half-closed intervals (-inf, -1/4] and [7/2, +inf)

========= -1/4 -------- 0 ------------------------------ 7/2 ==============

Note. The 2 end points are included in the solution set

Answer 2 · 2016-03-19T04:42:44

x is outside the closed interval #[-1/2, 7/2]#. The domain is the real line sans #[-1/2, 7/2]#.

#|3-2x|>=4# is the combined equation for the couple
#3-2x>=4 and 2x-3>=4#.

From the first in the pair, #x<=-1/2#.
From the second, #x>=7/2#.