1) \(|5x-3|=|7-x|\)

\(\Leftrightarrow\orbr{\begin{cases}5x-3=7-x\\5x-3=x-7\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}6x=10\\4x=-4\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{5}{3}\\x=-1\end{cases}}\)

Vậy...

2) \(2.|3x-1|-3x=7\)

\(\Leftrightarrow2.|3x-1|=7+3x\)

\(\Leftrightarrow\orbr{\begin{cases}2.\left(3x-1\right)=7+3x\\2.\left(3x-1\right)=-7-3x\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}6x-2=7+3x\\6x-2=-7-3x\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}3x=9\\9x=-5\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=3\\x=\frac{-5}{9}\end{cases}}\)

Vậy...

\(a,\left(x-\dfrac{1}{3}\right)\left(x+\dfrac{2}{3}\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=-\dfrac{2}{3}\end{matrix}\right.\\ b,\left(\dfrac{3}{4}x-\dfrac{9}{16}\right)\left(1,5+\dfrac{-3}{x}\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}\dfrac{3}{4}x=\dfrac{9}{16}\\-\dfrac{3}{x}=-1,5=-\dfrac{3}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{4}\\x=2\end{matrix}\right.\)

a: \(\left(x-\dfrac{1}{3}\right)\left(x+\dfrac{2}{3}\right)=0\)

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

b: \(\left(\dfrac{3}{4}x-\dfrac{9}{16}\right)\left(\dfrac{1}{5}+\left(-3\right):x\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{3}{4}x=\dfrac{9}{16}\\\left(-3\right):x=-\dfrac{1}{5}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{9}{16}:\dfrac{3}{4}=\dfrac{9}{16}\cdot\dfrac{4}{3}=\dfrac{3}{4}\\x=\left(-3\right):\dfrac{-1}{5}=15\end{matrix}\right.\)

c) Ta có: \(\left\{{}\begin{matrix}\left|x-1,5\right|\ge0\forall x\in Q\\\left|2,5-x\right|\ge0\forall x\in Q\end{matrix}\right.\)

\(\Rightarrow\left|x-1,5\right|+\left|2,5-x\right|\ge0\forall x\in Q\)

Dấu "=" xảy ra khi \(\left\{{}\begin{matrix}\left|x-1,5\right|=0\\\left|2,5-x\right|=0\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x=1,5\\x=2,5\end{matrix}\right.\)

Vậy \(x=\left\{{}\begin{matrix}1,5\\2,5\end{matrix}\right.\).

e) \(\left(x-2\right)^2=1\)

\(\Rightarrow\left[{}\begin{matrix}x-2=\sqrt{1}\\x-2=-\sqrt{1}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)

Vậy \(\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\).

Mấy câu kia dễ rồi.

sửa lại ý c của N.Anh

Áp dụng bđt \(\left|a\right|+\left|b\right|\ge\left|a+b\right|\) có:

\(\left|x-1,5\right|+\left|2,5-x\right|\ge\left|x-1,5+2,5-x\right|=1\)

\(\Rightarrow\left|x-1,5\right|+\left|2,5-x\right|\ge1>0\)

mà theo đề thì \(\left|x-1,5\right|+\left|2,5-x\right|=0\)

\(\Rightarrow\) k có gt \(x\) nào tm yêu cầu đề bài

a) \(\left(x-1,3\right)^2=9\Leftrightarrow\left[{}\begin{matrix}x-1,3=3\\x-1,3=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4,3\\x=-1,7\end{matrix}\right.\)

b) 2^4-x = 32

⇔ 2^4-x = 2⁵

⇔ 4-x=5

⇔ x=-1

c) (x+1,5)²+(y-2,5)¹⁰=0

\(\Leftrightarrow\left\{{}\begin{matrix}x+1,5=0\\y-2,5=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-1,5\\y=2,5\end{matrix}\right.\)

\(a,\left(x-1,3\right)^2=9\\ \Leftrightarrow\left(x-1,3+9\right)\left(x-1,3-9\right)=0\\ \Leftrightarrow\left(x-7,7\right)\left(x-10,3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=7,7=\dfrac{77}{10}\\x=10,3=\dfrac{103}{10}\end{matrix}\right.\)

\(b,2^{4-x}=32=2^5\\ \Leftrightarrow4-x=5\\ \Leftrightarrow x=-1\)

\(c,\left(x+1,5\right)^2+\left(y-2,5\right)^{10}=0\\ \Leftrightarrow\left\{{}\begin{matrix}x+1,5=0\\y-2,5=0\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=-1,5=-\dfrac{3}{2}\\y=2,5=\dfrac{5}{2}\end{matrix}\right.\)

a) làm mẫu cho cả phần b lun

 \(|2x-5|+|2,5-x|=0\left(1\right)\)

Ta có: \(2x-5=0\Leftrightarrow x=\frac{5}{2}\)

          \(2,5-x=0\Leftrightarrow x=2,5=\frac{5}{2}\)

Lập bảng xét dấu :

+) Với \(x< \frac{5}{2}\Rightarrow\hept{\begin{cases}2x-5< 0\\2,5-x< 0\end{cases}\Rightarrow}\hept{\begin{cases}|2x-5|=5-2x\\|2,5-x|=x-2,5\end{cases}}\left(2\right)\)

Thay (2) vào (1) ta được :

\(5-2x+x-2,5=0\)

\(-x+\frac{5}{2}=0\)

\(x=\frac{5}{2}\)( loại ) 

+) Với \(x\ge\frac{5}{2}\Rightarrow\hept{\begin{cases}2x-5\ge0\\2,5-x\ge0\end{cases}\Rightarrow}\hept{\begin{cases}|2x-5|=2x-5\\|2,5-x|=2,5-x\end{cases}}\left(3\right)\)

Thay (3) vào (1) ta được :

\(2x-5+2,5-x=0\)

\(x-\frac{5}{2}=0\)

\(x=\frac{5}{2}\)( chọn )

Vậy \(x=\frac{5}{2}\)

a) |2x - 5| + |2,5 - x| = 0

2x - 5 = 0 hoặc 2,5 - x = 0

2x = 0 + 5         -x = 0 - 2,5

2x = 5               -x = -2,5

x = 2,5               x = 2,5

=> x = 2,5

b) |x - 1,5| + |x + 3| = 0

x - 1,5 = 0 hoặc x + 3 = 0

x = 0 + 1,5         x = 0 - 3

x = 1,5               x = -3

=> x = 1,5 hoặc x = -3

c) (5x - 2)² = 1

(5x - 2)² = 1²

5x - 2 = 1; -1

5x - 2 = 1 hoặc 5x - 2 = -1

5x = 1 + 2         5x = -1 + 2

5x = 3               5x = 1

x = 3/5              x = 1/5

=> x = 3/5 hoặc x = 1/5

d) (4x - 1)³ + 7 = -20

(4x - 1)³ = -20 - 7

(4x - 1)³ = -27

(4x - 1)³ = (-3)³

4x - 1 = -3

4x = -3 + 1

4x = -2

x = -2/4 = -1/2