Question

Tìm x:

a)2./x-2/=/-18/

b)/2x-3/-/-2/=15

Answer 1

a) \(2\cdot\left|x-2\right|=\left|-18\right|\)

\(\Rightarrow\left|x-2\right|=9\)

\(\Rightarrow\left[{}\begin{matrix}x=11\\x-7\end{matrix}\right.\)

b) \(\left|2x-3\right|-\left|-2\right|=15\)

\(\Rightarrow\left|2x-3\right|=17\)

\(\Rightarrow\left[{}\begin{matrix}x=10\\x=-7\end{matrix}\right.\)

Answer 2

a) 2.|x-2|=|-18|

2.|x-2|=18

|x-2|=18:2

|x-2|=9

\(\Rightarrow\left[{}\begin{matrix}x-2=9\\x-2=-9\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=11\\x=-7\end{matrix}\right.\)

Vậy x=11 hoặc x=-7

b) |2x-3|-|-2|=15

|2x-3|-2=15

|2x-3|=15+2

|2x-3|=17

\(\Rightarrow\left[{}\begin{matrix}2x-3=17\\2x-3=-17\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=20\\2x=-14\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=10\\x=-7\end{matrix}\right.\)

Vậy x=10 hoặc x=-7

Answer 3

a) \(2\cdot\left|x-2\right|=\left|-18\right|\)

\(2\cdot\left|x-2\right|=18\)

\(\left|x-2\right|=\dfrac{18}{2}\)

\(\left|x-2\right|=9\)

\(\Rightarrow\left[{}\begin{matrix}x-2=9\\x-2=-9\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=9+2\\x=\left(-9\right)+2\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=11\\x=-7\end{matrix}\right.\)

Vậy \(x\in\left\{11;-7\right\}\)

b) \(\left|2x-3\right|-\left|-2\right|=15\)

\(\left|2x-3\right|-2=15\)

\(\left|2x-3\right|=15+2\)

\(\left|2x-3\right|=17\)

\(\Rightarrow\left[{}\begin{matrix}2x-3=17\\2x-3=-17\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}2x=17+3\\2x=\left(-17\right)+3\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}2x=20\\2x=-14\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{20}{2}\\x=\dfrac{-14}{2}\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=10\\x=-7\end{matrix}\right.\)

Vậy \(x\in\left\{10;-7\right\}\)

Answer 4

a) 2. / x - 2 / = / - 18 /

\(\Rightarrow\) 2. /x - 2 / = 18

\(\Rightarrow\) / x - 2 / = 18 : 2

\(\Rightarrow\) / x - 2 / = 9

\(\Rightarrow\) \(\left[{}\begin{matrix}x-2=18\\x-2=-18\end{matrix}\right.\)

\(\Rightarrow\) \(\left[{}\begin{matrix}x=&20\\x=&-16\end{matrix}\right.\)

b) / 2x - 3 / - / -2 / = 15

\(\Rightarrow\) / 2x - 3 / - 2 = 15

\(\Rightarrow\) / 2x - 3 / = 17

\(\Rightarrow\) \(\left[{}\begin{matrix}2x-3=17\\2x-3=-17\end{matrix}\right.\)

\(\Rightarrow\) \(\left[{}\begin{matrix}2x=20\\2x=-14\end{matrix}\right.\)

\(\Rightarrow\) \(\left[{}\begin{matrix}x=10\\x=-7\end{matrix}\right.\)

Answer 5

a)2 . |x - 2| = |-18|

2 . |x - 2| = 18

|x - 2| = 18 : 2

|x - 2| = 9

⇒ \(\left\{{}\begin{matrix}x-2=9\\x-2=\left(-9\right)\end{matrix}\right.\)

⇒ \(\left\{{}\begin{matrix}\text{x = 9 + 2 }\\\text{x = (-9) + 2}\end{matrix}\right.\)

⇒ \(\left\{{}\begin{matrix}x=11\\x=\left(-7\right)\end{matrix}\right.\)

Vậy x = 11 hay x = -7

b)|2x - 3| - |-2| = 15

|2x - 3| - 2 = 15

|2x - 3| = 15 + 2

|2x - 3| = 17

⇒ \(\left\{{}\begin{matrix}\text{2x - 3 = 17}\\\text{2x - 3 = (-17)}\end{matrix}\right.\)

⇒ \(\left\{{}\begin{matrix}2x=17+3=20\\2x=\left(-17\right)+3=\left(-14\right)\end{matrix}\right.\)

⇒ \(\left\{{}\begin{matrix}x=20:2=10\\x=\left(-14\right):2=\left(-7\right)\end{matrix}\right.\)

Vậy x = 10 hay x = -7