Question

Solve the absolute value equation. 20x - 19 = 0

Answer 1

To solve this absolute value equation, we can use find the solutions as follows taking into account the definition of absolute value, then, we have:

$|20x-19|=0\Rightarrow20x-19=0,or-(20x-19)=0$

Now, we can solve both equations to find the solution(s):

First case:

$20x-19=0\Rightarrow20x=19\Rightarrow x=\frac{19}{20}$

Second case:

$-(20x-19)=0\Rightarrow-20x+19=0\Rightarrow-20x=-19\Rightarrow x=-\frac{19}{-20}\Rightarrow x=\frac{19}{20}$

Then, both solutions are the same, because of the absolute rule (this is the point when y = 0, that is the x-intercept for this function.)

Therefore, the solution set is {19/20}.