Question

abs((1-2x)/x)=3x solve for x

Answer 1

\[|\frac{1-2x}{x}|=3x\] like that?

Answer 2

since absolute value is always greater than or equal to zero, we can assume that \(x\) is as well, otherwise there is no solution. therefore you can solve
\[\frac{1-2x}{x}=3x\] only in the case where \(x\geq 0\)

Answer 3

since \(x\neq 0\) and also we know \(x>0\) multiply both sides by \(x\) to get
\[1-2x=3x^2\]or
\[3x^2+2x-1=0\] and solve the quadratic

Answer 4

this one actually factors as \((3x-1)(x+1)=0\) so \(x=\frac{1}{3}\)
we can throw out the \(-1\) solution because it is negative and \(x\) cannot be negative

Answer 5

Thank you!

Answer 6

yw, hope steps are clear