Find the values of x in? |x-1|-|2x-5|=2x|x1||2x5|=2x

1 Answer
Jul 24, 2018

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

Explanation:

There are 22 points to consider

x-1=0x1=0, =>, x=1x=1

2x-5=02x5=0, =>, x=5/2x=52

There are 33 intervals to consider

I_1=(-oo,1)I1=(,1)

I_2=(1,5/2)I2=(1,52)

I_3=(5/2,+oo)I3=(52,+)

In the first interval I_1I1

-x+1+2x-5-2x=0x+1+2x52x=0

x=-4x=4

This solution in I_1I1

In the second interval I_2I2

x-1+2x-5-2x=0x1+2x52x=0

x=6x=6

This solution does not !inI_2I2

In the third interval I_3I3

x-1-2x+5-2x=0x12x+52x=0

3x=43x=4

x=4/3x=43

This solution does not !inI_3I3

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

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