Question

-8+2.|2.x-3|=4

. là nhân nhé

Answer 1

\(-8+2\left|2x-3\right|=4\)

\(\Leftrightarrow2\left|2x-3\right|=4-\left(-8\right)\)

\(\Leftrightarrow2\left|2x-3\right|=4+8\)

\(\Leftrightarrow2\left|2x-3\right|=12\)

\(\Leftrightarrow\left|2x-3\right|=12:2\)

\(\Leftrightarrow\left|2x-3\right|=6\)

Xét trường hợp 1: \(2x-3=6\)

\(\Rightarrow2x=6+3\)

\(\Rightarrow2x=9\)

\(\Rightarrow x=9:2\)

\(\Rightarrow x=\dfrac{9}{2}\)

Xét trường hợp 2: \(2x-3=-6\)

\(\Rightarrow2x=-6+3\)

​\(\Rightarrow2x=-\left(6-3\right)\)​

\(\Rightarrow2x=-3\)

\(\Rightarrow x=-3:2\)

\(\Rightarrow x=\dfrac{-3}{2}\)

Vậy \(x=\dfrac{9}{2}\) hoặc \(x=\dfrac{-3}{2}\)

Answer 2

-8+2.|2.x-3|=4

2.|2.x-3|=4-(-8)

2.|2.x-3|=12

|2.x-3|=12:2

|2.x-3|=6

TH1:2.x-3=6

2.x=6+3

2.x=9

x=9:2

x=4,5

TH2:2.-3=-6

2x=-6+3

2x=-3

x=-3:2

x=-1,5

Answer 3

-8+2.|2.x-3|=4

2.|2.x-3|=4-(-8)

2.|2.x-3|=12

|2.x-3|=12:2

|2.x-3|=6

TH1:2.x-3=6

2.x=6+3

2.x=9

x=9:2

x=4,5

TH2:2.-3=-6

2x=-6+3

2x=-3

x=-3:2

x=-1,5

Answer 4

-8+2.|2x-3|=4

⇒2.|2x-3|=4-(-8)=4+8

⇒2.|2x-3|=12

⇒|2x-3|=12:2=6

⇒\(\left\{{}\begin{matrix}2x-3=6\\2x-3=-6\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}2x=6+3=9\\2x=-6+3=-3\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=\dfrac{9}{2}\\x=\dfrac{-3}{2}\end{matrix}\right.\)

Vậy x∈{\(\dfrac{9}{2}\);\(\dfrac{-3}{2}\)}