Possible answer 1: x - 5 =2x
Subtract 2x from both sides
x−5 -2x =2x−2x
-x -5= 0
Add 5 to both sides.
-x -5 +5 = 0 +5
-x= 5
Divide both sides by -1.
-x/-1= 5/-1
X= -5
Possible answer 2: x -5 = -2x
Add 2x to both sides.
X -5 +2x = -2x +2x
3x -5 = 0
Add 5 to both sides.
3x -5 +5= 0+5
3x= 5
Divide both sides by 3.
3x/3= 5/3
X=5/3
These two are the possible answers but check if they work: x= -5, x= 5/3.
Plug them in the equation.
|x-5| =2x
Possible Answer 1: |-5-5| =2x
|-10|=2x
10=2x
Divide both sides by 2.
10/2=2x/2
5=x
This means the answer x=-5 doesn’t work since the result ended up being a positive 5. Thus, this is not a solution.
Possible answer 2: |5/3-5| =2x
5/3 subtracted by 5 is -10/3.
|-10/3| = 2x
10/3 =2x
Divide both sides by 2.
(10/3)/2= 2x/2
5/3 = x
This means the solution x=5/3 works. Thus, a solution.
The first one doesn’t work but the second one does. So that means possible answer 2 is the answer.
Answer: x= 5/3
I hope this is helpful.
