How do you solve #abs(5.2x+7)=3.8#?

1 Answer
Apr 3, 2017

Answer:

#x = -8/13, -27/13#

Explanation:

CASE 1. #color(red)(5.2x+7 >= 0)#

if
#5.2x+7 >= 0#
#i.e. x >= -7/5.2# or #x >= -35/26#

then
#|5.2x+7| = 5.2x+7#
because the modulus of a positive number is the number itself.

#therefore # in this case #5.2x+7=3.8# #=> 5.2x = -3.2#
#=> x=-3.2/5.2 = color(red)(-8/13)#

CASE 2. #color(red)(5.2x+7 < 0)#

if
#5.2x+7 < 0#
#i.e. x < -7/5.2# or #x < -35/26#

then
#|5.2x+7| = -(5.2x+7) = -5.2x-7#
because the modulus of a negative number is negative of the number or in other words modulus of a negative number is obtained by multiplying the number with #-1#.

#e.g. -2<0 => |-2| = -(-2) or -1*(-2) = 2#

#therefore # in this case #-5.2x-7=3.8# #=>-5.2x = 10.8#
#=> x=-10.8/5.2 = color(red)(-27/13)#

Hence, #x = color(red)(-8/13) or color(red)(-27/13)#.