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

2 Answers
May 19, 2017

Answer:

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

Explanation:

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

May 19, 2017

Answer:

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")#
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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#
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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 B