How do you graph and solve # |5x – 2|>=8#?

1 Answer
Jul 27, 2018

Answer:

See a solution process below:

Explanation:

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

Therefore we can write and solve this as:

#-8 >= 5x - 2 >= 8#

First, add #color(red)(2)# to each segment of the system of inequalities to isolate the #x# term while keeping the system balanced:

#-8 + color(red)(2) >= 5x - 2 + color(red)(2) >= 8 + color(red)(2)#

#-6 >= 5x - 0 >= 10#

#-6 >= 5x >= 10#

Now, divide each segment by #color(red)(5)# to solve for #x# while keeping the system balanced:

#-6/color(red)(5) >= (5x)/color(red)(5) >= 10/color(red)(5)#

#-6/5 >= (color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) >= 2#

#-6/5 >= x >= 2#

Or

#x <= -6/5#; #x >= 2#

Or

#(-oo, -6/5]#; #[2. +oo)#