Question

find the real valued solutions
|x-3|=|5x|

Answer 1

|x-3|=|5x|


x-3=5x, or -(x-3)=5x, or x-3=-5x or -(x-3)=-5x


Note: -(x-3)=5x is the same as x-3=-5x (after multiplying both sides by -1)

also, -(x-3)=-5x is the same as x-3=5x (again, after multiplying both sides by -1)



So we only have to solve 2 equations: x-3=5x and -(x-3)=5x


to get the answers

solve x-3=5x:

x-3=5x

-3=5x-x

-3=4x

-3/4 = x

x = -3/4


solve -(x-3)=5x


-(x-3)=5x


-x+3=5x

3 = 5x+x

3 = 6x

3/6 = x

1/2 = x

x= 1/2


So the answers are x = -3/4 or x = 1/2

Answer 2

thank you :)