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subjects
CTVHS
18 tháng 8 2025
\(a.\frac12+\frac32x=\frac34\)
\(\frac32x=\frac34-\frac12=\frac14\)
\(x=\frac14:\frac32=\frac14\cdot\frac23=\frac16\)
\(b.2,5-2\cdot\left(x-0,5\right)=2\)
\(2\cdot\left(x-0,5\right)=2,5-2=0,5\)
\(x-0,5=0,5:2=0,25\)
\(x=0,25+0,5=0,75\)
\(c.\left(x+\frac32\right)^3=\frac{125}{8}=\left(\frac52\right)^3\)
\(x+\frac32=\frac52\)
\(x=\frac52-\frac32=\frac22=1\)
\(d.\left(x-\frac13\right)^2=\frac{25}{4}=\left(\pm\frac52\right)^2\)
\(\left[\begin{array}{l}x-\frac13=\frac52\Rightarrow x=\frac{17}{6}\\ x-\frac13=-\frac52\Rightarrow x=-\frac{13}{6}\end{array}\right.\)
vậy \(x\in\left\lbrace\frac{17}{6};-\frac{13}{6}\right\rbrace\)
\(e.7\cdot3^{x-1}-3^{x+2}=-540\)
\(3^{x-1}\cdot\left(7-3^3\right)=-540\)
\(3^{x-1}\cdot\left(7-27\right)=-540\)
\(3^{x-1}\cdot\left(-20\right)=-540\)
\(3^{x-1}=\left(-540\right):\left(-20\right)\)
\(3^{x-1}=27=3^3\)
⇒ x - 1 = 3
⇒ x = 4
NV
2
NL
Nguyễn Lê Phước Thịnh
CTVHS
15 tháng 8 2025
1: ĐKXĐ: x<>1/2
Ta có: \(\frac{2x-1}{4}=\frac{4}{2x-1}\)
=>\(\left(2x-1\right)\left(2x-1\right)=4\cdot4\)
=>\(\left(2x-1\right)^2=16\)
=>\(\left[\begin{array}{l}2x-1=4\\ 2x-1=-4\end{array}\right.\Rightarrow\left[\begin{array}{l}2x=4+1=5\\ 2x=-4+1=-3\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\frac52\left(nhận\right)\\ x=-\frac32\left(nhận\right)\end{array}\right.\)
2: ĐKXĐ: x<>1/2
\(\frac{2x-1}{27}=\frac{3}{2x-1}\)
=>\(\left(2x-1\right)\left(2x-1\right)=27\cdot3=81\)
=>\(\left(2x-1\right)^2=81\)
=>\(\left[\begin{array}{l}2x-1=9\\ 2x-1=-9\end{array}\right.\Rightarrow\left[\begin{array}{l}2x=10\\ 2x=-8\end{array}\right.\Rightarrow\left[\begin{array}{l}x=5\left(nhận\right)\\ x=-4\left(nhận\right)\end{array}\right.\)
3: ĐKXĐ: x∉{0;-1}
Ta có: \(\frac{4}{x}=\frac{8}{x+1}\)
=>\(\frac{1}{x}=\frac{2}{x+1}\)
=>2x=x+1
=>2x-x=1
=>x=1(nhận)
4: ĐKXĐ: x<>-5
Ta có: \(\frac{x-1}{x+5}=\frac67\)
=>7(x-1)=6(x+5)
=>7x-7=6x+30
=>7x-6x=7+30
=>x=37(nhận)
5: \(\frac{x-3}{5}=\frac{5-2x}{11}\)
=>11(x-3)=5(5-2x)
=>11x-33=25-10x
=>21x=25+33=58
=>\(x=\frac{58}{21}\)
6: ĐKXĐ: x∉{-1;-7}
Ta có: \(\frac{x}{x+1}=\frac{x+5}{x+7}\)
=>x(x+7)=(x+1)(x+5)
=>\(x^2+7x=x^2+6x+5\)
=>7x=6x+5
=>7x-6x=5
=>x=5(nhận)
7: ĐKXĐ: x∉{-2/5;-1/5}
ta có: \(\frac{2x+3}{5x+2}=\frac{4x+5}{10x+2}\)
=>(2x+3)(10x+2)=(5x+2)(4x+5)
=>\(20x^2+4x+30x+6=20x^2+25x+8x+10\)
=>34x+6=33x+10
=>34x-33x=10-6
=>x=4(nhận)
8: ĐKXĐ: x∉{-2;-8}
ta có: \(\frac{2x-18}{2x+4}=\frac{2x-17}{2x+16}\)
=>\(\frac{2\left(x-9\right)}{2\left(x+2\right)}=\frac{2x-17}{2x+16}\)
=>\(\frac{x-9}{x+2}=\frac{2x-17}{2x+16}\)
=>(2x-17)(x+2)=(x-9)(2x+16)
=>\(2x^2+4x-17x-34=2x^2+16x-9x-144\)
=>-13x-34=7x-144
=>-13x-7x=-144+34
=>-20x=-110
=>\(x=\frac{110}{20}=\frac{11}{2}\) (nhận)
15 tháng 8 2025
tất cả các câu đều là tỉ lệ thức nhé
Bài 3:
a: \(A=\left\lbrace\left\lbrack\left(\frac12-\frac23\right)^2:2\right\rbrack-\left(-3\right)^0\right\rbrace\cdot\frac23\)
\(=\left\lbrack\left(\frac36-\frac46\right)^2:2-1\right\rbrack\cdot\frac23\)
\(=\left\lbrack\left(-\frac16\right)^2:2-1\right\rbrack\cdot\frac23=\left(\frac{1}{36}\cdot\frac12-1\right)\cdot\frac23=\left(\frac{1}{72}-1\right)\cdot\frac23\)
\(=-\frac{71}{72}\cdot\frac23=-\frac{71}{36\cdot3}=-\frac{71}{108}\)
b: \(B=\left\lbrack\left(\frac25+1\right):\frac23\right\rbrack\cdot\left(\frac34-\frac18\right)^2\)
\(=\left\lbrack\frac75\cdot\frac32\right\rbrack\cdot\left(\frac68-\frac18\right)^2\)
\(=\frac{21}{10}\cdot\left(\frac58\right)^2=\frac{21}{10}\cdot\frac{25}{64}=\frac{21}{2}\cdot\frac{5}{64}=\frac{105}{128}\)
Bài 2:
a: \(\frac38\cdot1\frac13-\frac38\cdot3\frac13\)
\(=\frac38\left(1+\frac13-3-\frac13\right)\)
\(=-2\cdot\frac38=-\frac34\)
b: \(\left(-\frac59\right)\cdot\frac{3}{11}+\left(-\frac{8}{18}\right)\cdot\frac{3}{11}\)
\(=\frac{3}{11}\left(-\frac59-\frac49\right)\)
\(=\frac{3}{11}\cdot\frac{-9}{9}=-\frac{3}{11}\)
Bài 1:
a: \(\frac{25}{12}+\frac{-4}{12}=\frac{25-4}{12}=\frac{21}{12}=\frac74\)
b: \(\frac{-7}{15}-\frac{-2}{15}=-\frac{7}{15}+\frac{2}{15}=-\frac{5}{15}=-\frac13\)
c: \(\frac38+\frac{-14}{6}=\frac{9}{24}-\frac{56}{24}=\frac{9-56}{24}=\frac{-47}{24}\)
d: \(3\frac14-1\frac13=\frac{13}{4}-\frac43\)
\(=\frac{39}{12}-\frac{16}{12}=\frac{39-16}{12}=\frac{23}{12}\)
e: \(\frac23+\frac{-10}{6}+\frac{-4}{3}=\frac23-\frac53-\frac43=\frac{-7}{3}\)
f: \(\frac73-\left(-\frac14-\frac{5}{12}\right)=\frac73+\frac14+\frac{5}{12}\)
\(=\frac{28}{12}+\frac{3}{12}+\frac{5}{12}=\frac{28+3+5}{12}=\frac{36}{12}=3\)
g: \(-\frac43:\frac{13}{9}=-\frac43\cdot\frac{9}{13}=\frac{-4}{13}\cdot3=-\frac{12}{13}\)
h: \(-\frac57\cdot\frac{49}{3}:\frac{-7}{6}=\frac57\cdot\frac{49}{3}\cdot\frac67=\frac53\cdot6=10\)
easy toi se giup ban 🤫🤫🤫🤫🤫🤫🤫🤫🤫🤫🤫🤫🤫🤫🤫🤫🤫🤫