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\(42x-3=32x+4\)
\(\Rightarrow42x-32x=3+4\)
\(\Rightarrow10x=7\)
\(\Rightarrow x=\frac{7}{10}\)

\(\Leftrightarrow2\left(2x-3\right)=5\left(x+4\right)\)
=>5x+20=4x-6
=>x=-26

Này bạn tớ ko bít làm câu đầu , to bít làm mỗi câu 2 thui mong bn thông cảm
5x - 1 = 2x - 4
=>5x - 2x = - 4 +1
=> 3x = - 3
=> x = - 3 : 3
=> x = -1
xy + 7x - 3y = 32
(xy + 7x) - (3y + 21) = 11
x(y + 7) - 3(y + 7) = 11
(y + 7)(x - 3) = 11
\(\Rightarrow\)y +7 , x - 3 \(\in\)Ư(11) = {1; -1; 11; -11}
Với y + 7 = 1 \(\Rightarrow\)y = -6 thì x - 3 = 11 \(\Rightarrow\)x = 14
y + 7 = -1 \(\Rightarrow\)y = -8 thì x - 3 = -11 \(\Rightarrow\)x = -8
y + 7 = 11 \(\Rightarrow\)y = 3 thì x - 3 = 1\(\Rightarrow\)x = 4
y + 7 = -11 \(\Rightarrow\)y = -18 thì x - 3 = -1 \(\Rightarrow\)x = 2
Vậy có 4 cặp x,y thỏa mãn (14,-6); (-8,-8); (4,3); (2,-18)

\(32\left(\frac{1}{8.11}+\frac{1}{11.14}+\frac{1}{14.17}+...+\frac{1}{197.200}\right)-x=\frac{1}{2}\)
\(\frac{32}{3}\left(\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}+....+\frac{3}{197.200}\right)-x=\frac{1}{2}\)
\(\frac{32}{3}\left(\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+...+\frac{1}{197}-\frac{1}{200}\right)-x=\frac{1}{2}\)
\(\frac{32}{3}\left(\frac{1}{8}-\frac{1}{200}\right)-x=\frac{1}{2}\)
x=0.78

A/\(\left(2,8x-32\right):\frac{2}{3}=-90\)
\(\left(\frac{28}{10}x-32\right)=\frac{-90}{1}.\frac{2}{3}\)
\(\left(\frac{14}{5}x-32\right)=\frac{-30}{1}.\frac{2}{1}\)
\(\left(\frac{14}{5}x-32\right)=-60\)
\(\frac{14}{5}x=-60+32\)
\(\frac{14}{5}x=-28\)
\(x=\frac{-28}{1}:\frac{14}{5}\)
\(x=\frac{-28}{1}.\frac{5}{14}\)
\(x=\frac{-2}{1}.\frac{5}{1}=-10\)
B/\(\left(4,5-2x\right).1\frac{4}{7}=\frac{11}{14}\)
\(\left(\frac{45}{10}-2x\right).\frac{11}{7}=\frac{11}{14}\)
\(\left(\frac{9}{2}-2x\right)=\frac{11}{14}:\frac{11}{7}\)
\(\left(\frac{9}{2}-2x\right)=\frac{11}{14}.\frac{7}{11}\)
\(\left(\frac{9}{2}-2x\right)=\frac{1}{2}.\frac{1}{1}=\frac{1}{2}\)
\(2x=\frac{9}{2}-\frac{1}{2}\)
\(2x=\frac{8}{2}\)
\(x=\frac{8}{2}:\frac{2}{1}=\frac{8}{2}.\frac{1}{2}\)
\(x=\frac{4}{2}.\frac{1}{1}=\frac{4}{2}=2\)

\(A=\dfrac{32}{x^2+2x+4}=\dfrac{32}{x^2+2x+1+3}=\dfrac{32}{\left(x^2+2x+1\right)+3}\)
= \(\dfrac{32}{\left(x+1\right)^2+3}\)
do (x+1)2 ≥ 0 ∀x
=> (x+1)2+3 ≥ 3
=> \(\dfrac{32}{\left(x+1\right)^2+3}\le\dfrac{32}{3}\)
=> A ≤ \(\dfrac{32}{3}\)
max A= \(\dfrac{32}{3}\) dấu "=" xảy ra khi
x+1=0
=> x=-1
vậy max A= \(\dfrac{32}{3}\) khi x=-1

Tìm x :
a) (2x + 1 )^4 = 16
<=> ( 2x + 1 )^4 = 4^2 hoặc (-4)^2
<=> 2x + 1 = 4 hoặc 2x + 1 = -4
<=> 2x = 3 hoặc 2x = -5
<=> x = 3/2 hoặc x = -5/2
Vậy x € { 3/2 ; -5/2 }
b) x^20 = x
<=> x^20 - x = 0
<=> x^19 . x^1 - x . 1 = 0
<=> x^19 . x - x . 1 = 0
<=> x . ( x^19 - 1 ) = 0
<=> x = 0 hoặc x^19 - 1 = 0
<=> x = 0 hoặc x^19 = 1
<=> x = 0 hoặc x^19 = 1^19
<=> x = 0 hoặc x = 1
Vậy x € { 0 ; 1 }
c) 5^x . 5^x+2 = 650
<=> 5^x . 1 + 5^x . 5^2 = 650
<=> 5^x . 1 + 5^x . 25 = 650
<=> 5^x . ( 1 + 25 ) = 650
<=> 5^x . 26 = 650
<=> 5^x = 25
<=> 5^x = 5^2
=> x = 2
d)32 < 2^x < 128
<=> 2^5 < 2^x < 2^7
=> 5 < x < 7
<=> 5 < 6 < 7
=> x = 6
e) 4< 2^x < 32
<=> 2^2 < 2^x < 2^5
=> 2 < x < 5
<=> 2 < 3 ; 4 < 5
=> x € { 3 ; 4 }

32:(2x+1)=32
=>\(2x+1=\frac{32}{32}=1\)
=>2x=1-1=0
=>x=0
32 : [ 2\(x\) + 1] = 32
2\(x+1\) = 32 : 32
2\(x\) + 1 = 1
2\(x\) = 1- 1
2\(x\) = 0
\(x\) = 0
Vậy \(x=0\)