How do you solve the equation #abs(7x-1)+2=0#?

1 Answer
Apr 16, 2018

Answer:

No solution

Explanation:

The #|cdot|# notation refers to the absolute value, or changing whatever is inside to its distance from #0# on a graph. For example, #|3|=3# and #|-3|=3#. The result is always positive.

Considering the equation, we can slightly rearrange it to
#|7x-1|+2=0#
#|7x-1|=-2#

Now, no matter what #x# is (real, imaginary, complex, etc.), the absolute value of #7x-1# will always be positive and can never be equal to #-2#.

Thus, there is no solution to the equation.

Now, if the equation was instead
#|7x-1|=2#
we would have to consider the case that #7x-1=2# and the case that #7x-1=-2# to arrive at the different possible solutions.