How do you solve #-5abs(4y-11)-3=12#?

2 Answers
Sep 1, 2016

Answer:

No solution.

Explanation:

#-5|4y-11|-3=12# can be written as

#-5|4y-11|=12+3=15#

or #|4y-11|=15/-5=-3#

As absolute value of a number cannot be negative there is no solution.

Sep 1, 2016

Answer:

The solution of #x# is #[7/4,2]#

Explanation:

This is an Inequatlity problem. The general forms is:
#abs(x-a)=b#
#-b<=(x-a)<=b#
#(a-b)<=x<=(a+b)#
Thus, #x# has a solution range #[#(a-b)#,#(a+b)#]#

The solution to this problem goes like:

#-5abs(4y-11)-3=12# ;or
#-5abs(4y-11)=15# ;or
#abs(4y-11)=-3# ;or
#-(-3)<=4y-11<=-3# ;or
#(11+3)<=4y<=(11-3)# ;or
#14<=4y<=8# ;or
#7/4<=y<=2#
Thus, the solution range of #x# is #[7/4,2]#