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

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Answer 1 · 2018-07-24T14:05:04

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

There are $2$ $2$ points to consider

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

$2 x - 5 = 0$ $2x-5=0$ , $\Rightarrow$ $=>$ , $x = \frac{5}{2}$ $x=5/2$

There are $3$ $3$ intervals to consider

$I_{1} = (- \infty, 1)$ $I_1=(-oo,1)$

$I_{2} = (1, \frac{5}{2})$ $I_2=(1,5/2)$

$I_{3} = (\frac{5}{2}, + \infty)$ $I_3=(5/2,+oo)$

In the first interval $I_{1}$ $I_1$

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

$x = - 4$ $x=-4$

This solution $\in I_{1}$ $in I_1$

In the second interval $I_{2}$ $I_2$

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

$x = 6$ $x=6$

This solution does not $\notin I_{2}$ $!inI_2$

In the third interval $I_{3}$ $I_3$

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

$3 x = 4$ $3x=4$

$x = \frac{4}{3}$ $x=4/3$

This solution does not $\notin I_{3}$ $!inI_3$

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

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