How do you solve #|-4x + 10| ≤ 46#?

2 Answers
Shiva Prakash M V
Aug 6, 2018

The solution is
For all values above 9 and less than or equal to 14, the relation is valid

Explanation:

#abs(-4x+10)<=46#
#-4x+10<=46#
#-4x<=46-10#
#-4x<=36#
#-x<=36/4#
#-x<=9#
#x>9#
or
#-4x+10<=-46#
#-4x<=-46-10#
#-4x<=-56#
#4x<=56#
#x<=56/4#
#x<=14#
The solution is
#x>9,x<=14#
For all values above 9 and less than or equal to 14, the relation is valid

Narad T.
Aug 6, 2018

The solution is #x in [-9,14]#

Explanation:

The inequality is

#|-4x+10|<=46#

The solution is

#{(4x-10<=46),(-4x+10<=46):}#

#<=>#, #{(4x<=46+10),(4x>=10-46):}#

#<=>#, #{(4x<=56),(4x>=-36):}#

#<=>#, #{(x<=56/4),(x>=-36/4):}#

#<=>#, #{(x<=14),(x>=-9):}#

The solution is

#x in [-9,14]#

graph{|4x-10|-46 [-105.4, 105.4, -52.7, 52.7]}

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