Find the values of x in? $|x-1|-|2x-5|=2x$

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Answer 1 · 2018-07-24T14:05:04

There is only one solution $x=-4$ .

There are $2$ points to consider

$x-1=0$ , $=>$ , $x=1$

$2x-5=0$ , $=>$ , $x=5/2$

There are $3$ intervals to consider

$I_1=(-oo,1)$

$I_2=(1,5/2)$

$I_3=(5/2,+oo)$

In the first interval $I_1$

$-x+1+2x-5-2x=0$

$x=-4$

This solution $in I_1$

In the second interval $I_2$

$x-1+2x-5-2x=0$

$x=6$

This solution does not $!inI_2$

In the third interval $I_3$

$x-1-2x+5-2x=0$

$3x=4$

$x=4/3$

This solution does not $!inI_3$

There is only one solution $x=-4$

graph{|x-1|-|2x-5|-2x [-18.02, 18.02, -9.01, 9.02]}

Find the values of x in? |x-1|-|2x-5|=2x |x-1|-|2x-5|=2x