How do you solve #abs(6x+7)=5x+2#?

1 Answer
Apr 1, 2015

#x=-9/11#

The absolute value operation does:

1 - If the inner value of absolute value is non-negative, it returns the value.

2- If the inner value of absolute value is negative, it returns #(-1)# times of the value.

Our given equality is:

#abs(6x+7)=5x+2#

  • If #6x+7 >=0# then absolute value opeariton will return #6x+7#

#6x+7=5x+2#
#x=-5#

There is an important trick when it comes to absolute value operation. Always test the result with the if condition.

#6*(-5)+7>=0# fails. So #-5# is not in the solution set.

  • If #6x+7<0# then absolute value opeariton will return #-(6x+7)#

#-6x-7 = 5x+2#
#-9=11x#
#-9/11=x#

Again, lets test the if condition.

#6*(-9/11)+7<0# success!

So #x=-9/11#