MHB What are the solutions to this absolute value equation?

[Alexstrasuz1]

I have trouble solving this equation
|1/2x+1|=|x|

My answers are x=2 and x=-2/3

 

[chisigma]

corrected mistake in (2) as pointed out by MarkFL in the successive post...

I have trouble solving this equation
|1/2x+1|=|x|

My answers are x=2 and x=-2/3

An easy way is to find the solution of the equations...

$\displaystyle \frac{1}{2 x} + 1 = x \implies 2\ x^{2} - 2\ x - 1 =0 \implies x = \frac{1 \pm \sqrt{3}}{2}\ (1)$

$\displaystyle \frac{1}{2 x} + 1 = - x \implies 2\ x^{2} + 2\ x + 1 =0 \implies x = \frac{- 1 \pm i}{2}\ (2)$

Kind regards

$\chi$ $\sigma$

P.S. MarlFL has 'discovered' a mistake in (2) and I corrected it... sorry!...

 

[MarkFL]

An easy way is to find the solution of the equations...

$\displaystyle \frac{1}{2 x} + 1 = x \implies 2\ x^{2} - 2\ x - 1 =0 \implies x = \frac{1 \pm \sqrt{3}}{2}\ (1)$

$\displaystyle \frac{1}{2 x} + 1 = - x \implies 2\ x^{2} + 2\ x - 1 =0 \implies x = \frac{- 1 \pm \sqrt{3}}{2}\ (2)$

Kind regards

$\chi$ $\sigma$

The second equation should be:

$$2x^2+2x+1=0\implies x=\frac{-1\pm i}{2}$$

 

[RLBrown]

I have trouble solving this equation
|1/2x+1|=|x|

My answers are x=2 and x=-2/3

Yes, your answers are correct.
Other posts were solving...
|1/2/x+1|=|x|

 

[MarkFL]

Yes, your answers are correct.
Other posts were solving...
|1/2/x+1|=|x|

Just to be clear, I was solving:

$$\left|\frac{1}{2x}+1\right|=|x|$$

More often than not, when someone uses 1/2x, they mean 1/(2x) as opposed to (1/2)x.

This is why is is better to use bracketing symbols (or even better, use $\LaTeX$) to remove doubt. :D