# 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: