Question

tính |x-1| + 3 = 2x

Answer 1

+ TH1 : x < 1 ta có :

/ x - 1 / + 3 = 2x

<=> -( x - 1 ) + 3 = 2x

<=> -x + 1 + 3 = 2x

<=> 3x = 4 <=> x = 4/3 ( KTM )

+ TH2 : x >= 1 ta có :

/ x - 1 / + 3 =2x

<=> x - 1 + 3 =2x

<=> x = 2 ( TM )

Answer 2

tính |x-1| + 3 = 2x

\(\left|x-1\right|+3=2x\) ( * )

Ta có: \(\left|x-1\right|=x-1\) nếu x-1 \(\ge\)0 \(\Leftrightarrow x\ge1\)

Khi đó ( * ) trở thành :

\(x-1+3=2x\)

\(\Leftrightarrow\) x-2x = 1-3

\(\Leftrightarrow\) -x = -2

\(\Leftrightarrow\) x=2 (tm)

Ta có : \(\left|x-1\right|\)=-(x-1) nếu x-1 < 0 \(\Leftrightarrow\)x <1

Khi đó ( * ) trở thành :

-x+1+3=2x

\(\Leftrightarrow\) -x-2x = -1-3

\(\Leftrightarrow\) -3x = -4

\(\Leftrightarrow\) x = \(\frac{4}{3}\)(không tm)

Vậy S = { 2 }