How do you graph and solve # 3|x-1|+2>=8#?
1 Answer
Dec 15, 2015
Explanation:
#|x| >= k => " " x>= k " " or " " " x<= -k#
#|x| <= k => " " k <=x <= k#
Given:
Isolate the inequality, so absolute value can be by itself.
Step 1: Subtract 2 to both side
#3|x-1|+cancel(2 color(red)(- 2)) >= 8 color(red)(- 2)#
#3|x-1| >= 6#
Step 2 : Divide by 3 to both side
#(3|x-1|)/color(blue)(3) >= 6/color(blue)(3)#
#|x-1| >= 2#
Step 3 : Undo the absolute value like the information mention at the beginning
#=>x-1 >= 2 " " " " or " " " " x-1 <= -2#
Step 4 : Solve for
# x >= 3 " " " or " " " x<= -1#
Step 5: Draw the number line and determine the interval from Step 4.
Solution: