How do you graph and solve #| 5x - 1 | <= 14#?

1 Answer
Mar 3, 2018

Answer:

#"See the Explanation"#

Explanation:

#|5x−1|≤14#

This means the distance from 5x - 1 to zero must be less than or equal to 14.
It can be rewritten as #-14 ≤ 5x−1 ≤14#

So, draw #y = -14# and # y = 14#, and #5x - 1#.
The answer is where the line 5x - 1 is in between -14 and 14 like the plot below:
https://www.desmos.com/calculator/psnq5dutum

And here we find the answer without graphing:
#-14 ≤ 5x−1 ≤14#
#-14 + 1≤ 5x ≤14+1#
#-13≤ 5x ≤15#
#-13/5≤ x ≤15/5#
#-2.6≤ x ≤3#

The answer is # [-2.6, 3]#