Modulus Functions 3

Submitted by roamingfree on Fri, 02/05/2021 - 11:43
skills
To complete this question, you need to be familiar with the modulus function and how to eliminate it to solve equations.
Question
Solve the equation below $$ |2x-4| = 3x $$
answer --- press button to toggle display
The answer is $x = \frac{4}{5}$
solution --- press button to toggle display
modulus function questionNote that for $x \lt 2, |2x-4| = -(2x-4) $ and for $x\gt 2, |2x-4| = 2x-4$ The original equation can admit at most two solutions, each as a solution to the linear equations below. $$ +(2x-4) = 3x, \;-(2x-4) = 3x $$ The first solution is $x = -4$ however, this is outside of the domain for which $|2x-4| = 2x-4$ and therefore isn't valid, the second is $x = \frac{4}{5}$, which falls in the domain for which $-(2x-4) = |2x-4|$ and so is the correct solution. Of course this question is far far easier if you just sketch the graph!