How do you solve #|5x | = | 3x - 8|#?
1 Answer
Consider the various cases of
Explanation:
Deduce piecewise domains of the equation
The modulus on the LHS changes behaviour at
Take the cases for the modulus on the LHS first:
If
If
Now for both of those, consider the two cases for the modulus on the RHS:
If
If
If
The final case never happens because the two conditions have zero overlap:
So we have an equation defined in three pieces according to ranges of
If
If
If
So it changes one way, then the other, as
Solve the equation on each domain
We have two different function forms - one of which applies to two of the domains.
Matching these to the domains above, we see that the correct equation has been solved for the answer that lies in
So we have two valid answers to the equation:
Sanity check the answer by overplotting the two sides of the graph, seeing that they cross at these values:
graph{(y-|5x|)(y-|3x-8|)=0 [-10, 10, -6.4, 33.6]}