How do you solve #5abs(q + 6)=20#?

2 Answers
Apr 3, 2015

#q=-2; q=-10#

Given: #5abs(q + 6) = 20#
#abs(q+6) = 4#

Absolute value is the distance a given number is from zero. This means that #q+6 = 4# or #q+6 = -4#

#q+6 =4#
#q = -2#

#q+6 = -4#
#q=-10#

I hope that was helpful.

Apr 3, 2015

Consider two possibilities:
#q<-6# and #q>-6#
(note by observation we can eliminate #q=-6#)

If #q<-6#
then #(q+6)# is negative and
#abs(q+6)# is equivalent to #-(q+6)#
and the equation becomes
#5 (-(q+6)) = 20#
#-q-6 = 4#
#q=-10#

If #q>-6#
then #(q+6)# is positive and
#abs(q+6)# is equivalent to #(q+6)#
and the equation becomes:
#5(q+6) = 20#
#q+6 = 4#
#q=-2#

The two solutions to this equation are
#q=-10# and #q=-2#