Question

[Nguyễn Huyền Trang]

a) |9 + x| = 2x

b) |5x|-3x=2

c) |x+6| -9 =2x

d) |2x-3| + x =21

e) |4 + 2x| = -4x

i) |3x -1| +2 = x

g) |x+15| +1 = 3x

h) | 2x -5| +x =2

Answer 1

[Trần Thanh Phương]

a) \(\left|x+9\right|=2x\)

\(\Leftrightarrow\left[{}\begin{matrix}x+9=2x\\x+9=-2x\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=9\\x=-3\end{matrix}\right.\)

b) \(\left|5x\right|-3x=2\Leftrightarrow\left|5x\right|=3x+2\)

\(\Leftrightarrow\left[{}\begin{matrix}5x=3x+2\\-5x=3x+2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\frac{-1}{4}\end{matrix}\right.\)

c) \(\left|x+6\right|-9=2x\Leftrightarrow\left|x+6\right|=2x+9\)

\(\Leftrightarrow\left[{}\begin{matrix}x+6=2x+9\\-x-6=2x+9\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=-5\end{matrix}\right.\)

d) \(\left|2x-3\right|+x=21\Leftrightarrow\left|2x-3\right|=21-x\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-3=21-x\\2x-3=x-21\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8\\x=-18\end{matrix}\right.\)

e) \(\left|2x+4\right|=-4x\)

\(\Leftrightarrow\left[{}\begin{matrix}2x+4=4x\\2x+4=-4x\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=\frac{-2}{3}\end{matrix}\right.\)

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

\(\Leftrightarrow\left[{}\begin{matrix}3x-1=x-2\\3x-1=2-x\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{-1}{2}\\x=\frac{3}{4}\end{matrix}\right.\)

g) \(\left|x+15\right|+1=3x\Leftrightarrow\left|x+15\right|=3x-1\)

\(\Leftrightarrow\left[{}\begin{matrix}x+15=3x-1\\x+15=1-3x\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8\\x=-3,5\end{matrix}\right.\)

h) \(\left|2x-5\right|+x=2\Leftrightarrow\left|2x-5\right|=2-x\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-5=2-x\\2x-5=x-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{7}{3}\\x=3\end{matrix}\right.\)

Answer 2

[Quốc Đạt]

a) |9+x|=2x

TH1: 9+x=2x

<=> 9=2x-x

<=> x=9

TH2: -9-x=2x

<=> -9=3x

<=> x=-3

b) |5x|-3x=2

TH1: 5x-3x=2

<=> 2x=2

<=> x=1

TH2: -5x-3x=2

<=> -8x=2

<=>x=-4

c) |x+6|-9=2x

TH1: x+6-9=2x

<=> -3=x

TH2: -x-6-9=2x

<=> -15=3x

<=>x=-5

d) |2x-3|+x=21

TH1: 2x-3+x=21

<=> 3x=24

<=> x=8

TH2: -2x+3+x=21

<=> -x=18

<=> x=-18

e,i,g,h tương tự