How do you solve the inequality abs(4x+7)< -3?

2 Answers
May 19, 2017

No solution , since | 4x + 7| >= 0

Explanation:

|4x +7 | < -3 . No solution , since | 4x + 7| >= 0

May 19, 2017

Is this question correct?
Assumption: The question is meant to read |4x+7|<+3

With this assumption I get " "-5/2 < x < -1

Explanation:

color(brown)("By definition the outcome of "|4x+7|" can only be positive.")

color(brown)("Thus it is not possible for the outcome to be less than negative 3")
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Assumption: The question is meant to read |4x+7|<+3

For this to be true we have: |+-3|=+3

Case 1: " "4x+7=-3

" "4x=-10
" "x=-5/2

Case 2: " "4x+7=+3

" "4x=-4
" "x=-1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This very likely defines a range of possible values that are between but not including x=-1 and x=-5/2" " =>" " -5/2 < x < -1

Lets test this by selecting values outside this domain

Set x=-6/2 giving |4(-6/2)+7|" " =" "|-12+7|=4 " not"<3

color(white)()

Set x=-9/10 giving
|4(-9/10)+7|" "=" " |-18/5+7|" "=" "+3 2/5" not" < 3
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(red)("Thus we have: " -5/2 < x < -1

Tony BTony B