How do you graph and solve #| 5x-4 |>34 #?

1 Answer
smendyka
Oct 17, 2017

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.

#-34 > 5x - 4 > 34#

#-34 + color(red)(4) > 5x - 4 + color(red)(4) > 34 + color(red)(4)#

#-30 > 5x - 0 > 38#

#-30 > 5x > 38#

#-30/color(red)(5) > (5x)/color(red)(5) > 38/color(red)(5)#

#-6 > (color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) > 38/5#

#-6 > x > 38/5# or #-6 > x > 7 3/5#

Or

#x < -6# and #x > 38/5#

Or, in interval notation:

#(-oo, -6)# and #(38/5, +oo)#

To graph this we will draw vertical lines at #-6# and #38/5# on the horizontal axis.

The lines will be dashed lines because the inequality operators do not contain an "or equal to" clause.

We will shade to the left and right side of the lines respectively:

enter image source here

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