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...

5) \(\text{1,6 - |x + 1,5| = 0}\)

\(|x + 1,5| = 1,6-0\)

\(\text{|x + 1,5| = 1,6}\)

\( |x | = 1,6-1,5\)

\(|x|=0,1\)

Câu 2 đây:

\(|x^2+|x-1||=x^2+2\)

\(\Rightarrow\orbr{\begin{cases}x^2+\left|x-1\right|=x^2+2\\x^2+\left|x-1\right|=-x^2-2\left(l\right)\end{cases}}\)

\(\Rightarrow\left|x-1\right|=2\Leftrightarrow\orbr{\begin{cases}x=3\\x=-1\end{cases}}\)

a)    \(M=\left(\frac{0,4-\frac{2}{9}+\frac{2}{11}}{1,4-\frac{7}{9}+\frac{7}{11}}-\frac{\frac{1}{3}-0,25+0,5}{1\frac{1}{6}-0,875+0,7}\right):\frac{2012}{2013}\)

\(=\left(\frac{\frac{2}{5}-\frac{2}{9}+\frac{2}{11}}{\frac{7}{5}-\frac{7}{9}+\frac{7}{11}}-\frac{\frac{1}{3}-\frac{1}{4}+\frac{1}{2}}{\frac{7}{6}-\frac{7}{8}+\frac{7}{10}}\right):\frac{2012}{2013}\)

\(=\left(\frac{2\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{11}\right)}{7\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{11}\right)}-\frac{2\left(\frac{1}{6}-\frac{1}{8}+\frac{1}{10}\right)}{7\left(\frac{1}{6}-\frac{1}{8}+\frac{1}{10}\right)}\right):\frac{2012}{2013}\)

\(=\left(\frac{2}{7}-\frac{2}{7}\right):\frac{2012}{2013}\)

\(=0\)

câu 2 đâu bn

... \(\Leftrightarrow\left|1,5-x\right|=0,25\Leftrightarrow\hept{\begin{cases}1,5-x=0,25\\1,5-x=-0,25\end{cases}\Leftrightarrow\hept{\begin{cases}x=1,5-0,25=1,25\\x=1,5+0,25=1,75\end{cases}}}\)Vậy........

/1.5-x=0,25-0

/1.5-x/=0,25

tường hợp 1

1.5-x=0,25

x=1,5-0,25=1,25

trường hợp 2

1,5-x=-0.25

x=1,5-(-0.25)=1,75

a, \(7\left(x-1\right)+2x\left(1-x\right)=0\)

\(\Rightarrow\left(7-2x\right)\left(x-1\right)=0\)

\(\Rightarrow\orbr{\begin{cases}7-2x=0\\x-1=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{7}{2}\\x=1\end{cases}}\)

b, \(0,25-\left|3,5-x\right|=0\)

\(\Rightarrow\left|3,5-x\right|=2,5\)

\(\Rightarrow\orbr{\begin{cases}3,5-x=2,5\\3,5-x=-2,5\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=1\\x=6\end{cases}}\)

c, \(\left|x+\frac{3}{4}\right|-\frac{1}{2}=0\)

\(\Rightarrow\left|x+\frac{3}{4}\right|=\frac{1}{2}\)

\(\Rightarrow\orbr{\begin{cases}x+\frac{3}{4}=\frac{1}{2}\\x+\frac{3}{4}=\frac{-1}{2}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{-1}{4}\\x=\frac{-5}{4}\end{cases}}\)

a) 7.(x-1) + 2x.(1-x) = 0

7.(x-1) - 2x.(x-1) = 0

(x-1).(7-2x) = 0

=> (x-1) = 0 => x = 1

7-2x = 0 => 2x = 7 => x = 7/2

KL:...

b) 0,25 - | 3,5-x| = 0

=> |3,5 - x| = 0,25

TH1: 3,5 - x = 0,25

x = 3,25

TH2: 3,5 - x = -0,25

x = 3,75

phần c bn dựa vào phần b mak lm nha

a) 7.(x - 1) + 2x.(1 - x) = 0

<=> -2x² + 9x - 7 = 0

<=> \(\orbr{\begin{cases}x=1\\x=\frac{7}{2}\end{cases}}\)

=> \(\orbr{\begin{cases}x=1\\x=\frac{7}{2}\end{cases}}\)

b) 0,25 - |3,5 - x| = 0

<=> - |3,5 - x| = 0 - 0,25

<=> - |3,5 - x| = -0,25 

<=> |3,5 - x| = 0,25

Ta xét 2 th:

Th1: |x| = 3,5 - 0,25

<=> |x| = \(\frac{13}{4}\)

Th2: |x| = 3,5 + 0,25

<=> x = \(\frac{15}{4}\)

=> \(\orbr{\begin{cases}x=\frac{13}{4}\\\frac{15}{4}\end{cases}}\)

c) \(\left|x+\frac{3}{4}\right|-\frac{1}{2}=0\)

<=> \(\left|x+\frac{3}{4}\right|=0+\frac{1}{2}\)

<=> \(\left|x+\frac{3}{4}\right|=\frac{1}{2}\)

Ta xét 2 th:

Th1: \(x+\frac{3}{4}=\frac{1}{2}\)

<=> \(x=\frac{1}{2}-\frac{5}{4}\)

<=> \(x=-\frac{3}{4}\)

Th2: \(x+\frac{3}{4}=\frac{1}{2}\)

<=> \(x=\frac{1}{2}-\frac{3}{4}\)

<=> \(x=-\frac{1}{4}\)

=> \(\orbr{\begin{cases}x=-\frac{3}{4}\\x=-\frac{1}{4}\end{cases}}\)

Lời giải:

a. $(x.0,25+1999).2000=(53+1999).2000$

$x.0,25.2000+1999.2000=53.2000+1999.2000$

$x.0,25.2000=53.2000$

$x.0,25=53$

$x=53:0,25=212$

b. 

$(5457+x:2):7=1075$

$5457+x:2=1075\times 7=7525$

$x:2=7525-5457=2068$

$x=2068\times 2=4136$

c. 

$1-(\frac{12}{5}+x-\frac{8}{9}): \frac{16}{9}=0$

$(\frac{12}{5}+x-\frac{8}{9}):\frac{16}{9}=1$

$\frac{12}{5}+x-\frac{8}{9}=1.\frac{16}{9}=\frac{16}{9}$

$\frac{68}{45}+x=\frac{16}{9}$

$x=\frac{16}{9}-\frac{68}{45}=\frac{4}{15}$

a: x=2/3-4/5=10/15-12/15=-2/15

b: 1/2-x=7/12

=>x=1/2-7/12=-1/12

c: =>7/2:x=-7/2

=>x=-1

d: =>1/6x=3/8-5/2=3/8-20/8=-17/8

=>x=-17/8*6=-102/8=-51/4

e: =>1,5x=-1,5

=>x=-1