Solve for x using the definition of the absolute value if:
5x-|2x-3|=8
My approach:
|2x-3|={2x-3 if x>0 or -(2x-3) if x<0
-|2x-3|=8-5x
Therefore, |2x-3|=5x-8
2x-3={5x-8 if x≥3/2 or -(5x-8) if x<3/2 //not sure if I wrote this correctly
Therefore 2x-3=5x-8
x=5/3 (valid)
Or
2x-3=-(5x-8)
x=11/7 (invalid)
5x-|2x-3|=8
My approach:
|2x-3|={2x-3 if x>0 or -(2x-3) if x<0
-|2x-3|=8-5x
Therefore, |2x-3|=5x-8
2x-3={5x-8 if x≥3/2 or -(5x-8) if x<3/2 //not sure if I wrote this correctly
Therefore 2x-3=5x-8
x=5/3 (valid)
Or
2x-3=-(5x-8)
x=11/7 (invalid)