c) -1/2-x=1/3 - 1/ -4
`#040911`
a,
\(\dfrac{1}{2}\cdot\left(x-4\right)-\dfrac{1}{4}\cdot\left(x-\dfrac{4}{3}\right)=2\cdot\left(x-\dfrac{1}{2}\right)\)
\(\Rightarrow\dfrac{1}{2}x-2-\dfrac{1}{4}x+\dfrac{1}{3}=2x-1\\\Rightarrow\left(\dfrac{1}{2}x-\dfrac{1}{4}x-2x\right)=2-\dfrac{1}{3}-1\\ \Rightarrow-\dfrac{7}{4}x=\dfrac{2}{3}\\ \Rightarrow x=\dfrac{2}{3}\div\left(-\dfrac{7}{4}\right)\\ \Rightarrow x=-\dfrac{8}{21}\)
Vậy, \(x=-\dfrac{8}{21}\)
b,
\(\dfrac{3}{4}-\left(x-\dfrac{1}{2}\right)^2=-\dfrac{11}{2}\)
\(\Rightarrow\left(x-\dfrac{1}{2}\right)^2=\dfrac{3}{4}-\left(-\dfrac{11}{2}\right)\\ \Rightarrow\left(x-\dfrac{1}{2}\right)^2=\dfrac{25}{4}\\ \Rightarrow\left(x-\dfrac{1}{2}\right)^2=\left(\pm\dfrac{5}{2}\right)^2\)
\(\Rightarrow\left[{}\begin{matrix}x-\dfrac{1}{2}=\dfrac{5}{2}\\x-\dfrac{1}{2}=-\dfrac{5}{2}\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}+\dfrac{1}{2}\\x=-\dfrac{5}{2}+\dfrac{1}{2}\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)
Vậy, \(x\in\left\{-2;3\right\}\)
c,
\(\dfrac{3}{16}+1\dfrac{1}{16}\cdot\left(x-\dfrac{2}{3}\right)^2=\dfrac{3}{4}\)
\(\Rightarrow\dfrac{17}{16}\cdot\left(x-\dfrac{2}{3}\right)^2=\dfrac{3}{4}-\dfrac{3}{16}\\ \Rightarrow\dfrac{17}{16}\cdot\left(x-\dfrac{2}{3}\right)^2=\dfrac{9}{16}\\ \Rightarrow\left(x-\dfrac{2}{3}\right)^2=\dfrac{9}{16}\div\dfrac{17}{16}\\ \Rightarrow\left(x-\dfrac{2}{3}\right)^2=\dfrac{9}{17}\)
Bạn xem lại đề có sai kh nhỉ?
c) \(\dfrac{3}{16}+\dfrac{1}{\dfrac{1}{16}}\left(x-\dfrac{2}{3}\right)^2=\dfrac{3}{4}\)
\(\Rightarrow16\left(x-\dfrac{2}{3}\right)^2=\dfrac{3}{4}-\dfrac{3}{16}\)
\(\Rightarrow16\left(x-\dfrac{2}{3}\right)^2=\dfrac{9}{16}\)
\(\Rightarrow\left(x-\dfrac{2}{3}\right)^2=\dfrac{9}{16}:16\)
\(\Rightarrow\left(x-\dfrac{2}{3}\right)^2=\dfrac{9}{256}=\left(\dfrac{3}{16}\right)^2\)
\(\Rightarrow\left[{}\begin{matrix}x-\dfrac{2}{3}=\dfrac{3}{16}\\x-\dfrac{2}{3}=-\dfrac{3}{16}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{16}+\dfrac{2}{3}\\x=-\dfrac{3}{16}+\dfrac{2}{3}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{41}{48}\\x=\dfrac{23}{48}\end{matrix}\right.\)
a, 2.x.(x-1)^2-3.x.(x+3).(x-3)-4.x.(x+1)^2
b,(a-b+c)^2-(b-c)^2+2.a.b-2.a.c
c,(3.x+1)^2-2.(1+3.x).(3.x+5)+(3.x+5)^2
d, (3+1).(3^2+1).(3^4+1).(3^8+1).(3^16+1).(3^32+1)
e, (a+b-c)^2+(a-b+c)^2+(b-c-a)^2+(c-a-b)^2
a,1/3 .(x-2/5)=3/4 b, 7/3:(x-2/3)=4/5 c,1/3.(x-2/5)=4/5 d, 2/3.(x-1/2)-1/4.(x-2/5)=7/3 e,3/7 .(x-2/3)+1/2=5/4.(x-2) f,1/2.(x-3)+1/3.(x-4)+1/4.(x-5)=1/5 g,[2/3.(x-1/2)-4/5]:(x-1/3)=21/5 h, {x-[1/2.(x-3)+11/5]}:(x-1/2)=3/5 i,x.(x-2/5)-(x+2).x+11/4=4/3
a: =>x-2/5=3/4:1/3=3/4*3=9/4
=>x=9/4+2/5=45/20+8/20=53/20
b: =>x-2/3=7/3:4/5=7/3*5/4=35/12
=>x=35/12+2/3=43/12
c: 1/3(x-2/5)=4/5
=>x-2/5=4/5*3=12/5
=>x=12/5+2/5=14/5
d: =>2/3x-1/3-1/4x+1/10=7/3
=>5/12x-7/30=7/3
=>5/12x=7/3+7/30=77/30
=>x=77/30:5/12=154/25
e: \(\Leftrightarrow x\cdot\dfrac{3}{7}-\dfrac{2}{7}+\dfrac{1}{2}-\dfrac{5}{4}x+\dfrac{5}{2}=0\)
=>\(x\cdot\dfrac{-23}{28}=\dfrac{2}{7}-3=\dfrac{-19}{7}\)
=>x=19/7:23/28=76/23
f: =>1/2x-3/2+1/3x-4/3+1/4x-5/4=1/5
=>13/12x=1/5+3/2+4/3+5/4=257/60
=>x=257/65
i: =>x^2-2/5x-x^2-2x+11/4=4/3
=>-12/5x=4/3-11/4=-17/12
=>x=17/12:12/5=85/144
c)5^x+1-5^x=20 c)2^x+2^x+4=544 c)4^2x+1+4^2x=80 c)3^2x+2+3^2x+1=108 c)7^x+3-7^x+1=16464
1) \(5^{x+1}-5^x=20\Leftrightarrow5^x\left(5-1\right)=20\Leftrightarrow5^x=5\Leftrightarrow x=1\)
2) \(2^x+2^{x+4}=544\Leftrightarrow2^x\left(1+2^4\right)=544\Leftrightarrow2^x=32\Leftrightarrow x=5\)
3) \(4^{2x+1}+4^{2x}=80\Leftrightarrow4^{2x}\left(4+1\right)=80\Leftrightarrow16^x=16\Leftrightarrow x=1\)
4) \(3^{2x+2}+3^{2x+1}=108\Leftrightarrow3^{2x}\left(3^2+3\right)=108\Leftrightarrow9^x=9\Leftrightarrow x=1\)
5) \(7^{x+3}-7^{x+1}=16464\Leftrightarrow7^x\left(7^3-7\right)=16464\Leftrightarrow7^x=49\Leftrightarrow x=2\)
c:Ta có: \(5^{x+1}-5^x=20\)
\(\Leftrightarrow5^x\cdot5-5^x=20\)
\(\Leftrightarrow5^x\cdot4=20\)
\(\Leftrightarrow5^x=5\)
hay x=1
c: Ta có: \(2^x+2^{x+4}=544\)
\(\Leftrightarrow2^x+2^x\cdot16=544\)
\(\Leftrightarrow2^x\cdot17=544\)
\(\Leftrightarrow2^x=32\)
hay x=5
c: Ta có: \(4^{2x+1}+4^{2x}=80\)
\(\Leftrightarrow16^x\cdot4+16^x=80\)
\(\Leftrightarrow16^x\cdot5=80\)
\(\Leftrightarrow16^x=16\)
hay x=1
c: Ta có: \(3^{2x+2}+3^{2x+1}=108\)
\(\Leftrightarrow9^x\cdot9+9^x\cdot3=108\)
\(\Leftrightarrow9^x\cdot12=108\)
\(\Leftrightarrow9^x=9\)
hay x=1
c: Ta có: \(7^{x+3}-7^{x+1}=16464\)
\(\Leftrightarrow7^x\cdot343-7^x\cdot7=16464\)
\(\Leftrightarrow7^x\cdot336=16464\)
\(\Leftrightarrow7^x=49\)
hay x=2
bài 3:
a) x - 3/4 = 6 x 3/8 b) 7/8 : x = 3 - 1/2 c) x + 1/2 x 1/3 = 3/4
d) 3/2 x 4/5 - x = 2/3 e) X x 3 1/3 = 3 1/3 : 4 1/4 f) 5 2/3 : x = 3 2/3 - 2 1/2
a) \(x-\dfrac{3}{4}=6\times\dfrac{3}{8}\)
\(x-\dfrac{3}{4}=\dfrac{9}{4}\)
=> \(x=\dfrac{9}{4}+\dfrac{3}{4}=3\)
b) \(\dfrac{7}{8}:x=3-\dfrac{1}{2}\)
\(\dfrac{7}{8}:x=\dfrac{5}{2}\)
=> \(x=\dfrac{7}{8}:\dfrac{5}{2}=\dfrac{7}{20}\)
c) \(x+\dfrac{1}{2}\times\dfrac{1}{3}=\dfrac{3}{4}\)
\(x+\dfrac{1}{6}=\dfrac{3}{4}\)
=> \(x=\dfrac{3}{4}-\dfrac{1}{6}=\dfrac{7}{12}\)
d) \(\dfrac{3}{2}\times\dfrac{4}{5}-x=\dfrac{2}{3}\)
\(\dfrac{6}{5}-x=\dfrac{2}{3}\)
=> \(x=\dfrac{6}{5}-\dfrac{2}{3}=\dfrac{8}{15}\)
e) \(x\times3\dfrac{1}{3}=3\dfrac{1}{3}:4\dfrac{1}{4}\)(?)
\(x\times\dfrac{10}{3}=\dfrac{40}{51}\)
=> \(x=\dfrac{40}{51}:\dfrac{10}{3}=\dfrac{4}{17}\)
f) \(5\dfrac{2}{3}:x=3\dfrac{2}{3}-2\)
\(\dfrac{17}{3}:x=\dfrac{5}{3}\)
=> \(x=\dfrac{17}{3}:\dfrac{5}{3}=\dfrac{17}{5}\)
a: =>x-3/4=18/8=9/4
=>x=9/4+3/4=12/4=3
b: =>7/8:x=5/2
=>x=7/8:5/2=7/8*2/5=14/40=7/20
c: x+1/2*1/3=3/4
=>x+1/6=3/4
=>x=3/4-1/6=9/12-2/12=7/12
d: =>12/10-x=2/3
=>6/5-x=2/3
=>x=6/5-2/3=18/15-10/15=8/15
e: =>x*10/3=10/3:17/4=10/3*4/17
=>x=4/17
f: =>17/3:x=13/3-5/2=26/6-15/6=11/6
=>x=17/3:11/6=17/3*6/11=34/11
a,3/2.(x-5/3)-4/5=x+1. b,1/6.(2x-3)=1/2.(-x+1/4)-2/3. c,-2/3.(x-1/4)=1/3.(2x-1). d,(x-1)^4=(x-1)^6. Chú ý: / có nghĩa là phần. ^ có nghĩa là dấu mũ. . có nghĩa là dấu nhân. Giúp mình với nha, cảm ơn các bạn
a/ \(\dfrac{3}{2}\left(x-\dfrac{5}{3}\right)+\dfrac{4}{5}=x+1\)
\(\Rightarrow\dfrac{3}{2}x-\dfrac{5}{2}-x=1+\dfrac{4}{5}\)
\(\Rightarrow\dfrac{3}{2}x-x=\dfrac{9}{5}+\dfrac{5}{2}\)
\(\Rightarrow\dfrac{1}{2}x=\dfrac{43}{10}\)
\(\Rightarrow x=\dfrac{43}{5}\)
b/ \(\dfrac{1}{6}\left(2x-3\right)=\dfrac{1}{2}\left(-x+\dfrac{1}{4}\right)-\dfrac{2}{3}\)
\(\Rightarrow\dfrac{1}{3}x-\dfrac{1}{2}=-\dfrac{1}{2}x+\dfrac{1}{8}-\dfrac{2}{3}\)
\(\Rightarrow\dfrac{1}{3}x+\dfrac{1}{2}x=\dfrac{1}{8}-\dfrac{2}{3}+\dfrac{1}{2}\)
\(\Rightarrow\dfrac{5}{6}x=-\dfrac{1}{24}\Rightarrow x=-\dfrac{1}{20}\)
c/ làm như b
d/ \(\left(x-1\right)^4=\left(x-1\right)^6\)
\(\Rightarrow\left[{}\begin{matrix}x-1=-1\\x-1=0\\x-1=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=1\\x=2\end{matrix}\right.\)
Vậy \(x\in\left\{0;1;2\right\}\)
Giải các phương trình sau bằng cách đưa về dạng ax + b = 0 :
1. a) 5 - (x - 6) = 4(3 - 2x)
b) 2x(x + 2)^2 - 8x^2 = 2(x - 2)( x^2 + 2x + 4)
c) 7 - (2x + 4) = - (x + 4)
d) (x - 2)^3 + (3x - 1)(3x + 1) = (x + 1)^3
e) (x + 1)(2x - 3) = (2x - 1)(x + 5)
f) (x - 1)^3 - x(x + 1)^2 = 5x(2 - x ) - 11(x +2)
g) (x-1) - (2x - 1 ) = 9 - x
h) (x-3)(x+4) - 2(3x - 2) = (x-4)^2
i) x(x+3)^2 - 3x = (x + 2)^3 + 1
j) (x + 1)(x^2 - x + 1) - 2x = x(x + 1)(x-1)
a) 5-(x-6)=4(3-2x)
<=>5-x+6-12+8x=0
<=>7x-1=0
=>x=1/7
Tính bằng 2 cách
a. 1/2 x 1/3 + 1/3 x 1/4
b. ( 3/4 + 1/2) x 2
c. 1/2 x 1/3 - 1/3 x 1/4
d. ( 4/3 - 1/2) x 2/3
a) 1/2x1/3 +1/3x1/4
cách 1: 1/2 x1/3+ 1/3 x1/4
=1/6 + 1/12
= 1/4
cách 2: 1/2 x1/3+ 1/3 x1/4
= 1/3x (1/2+1/4)
= 1/3x3/4
= 1/4
b) (3/4+ 1/2)x2
cách 1: (3/4+1/2)x2
= 5/4x2
= 5/4
cách 2: (3/4+1/2)x2
=3/4 x2 + 1/2x2
=3/2+2/2
= 5/4
a. \(\frac{1}{2}\times\frac{1}{3}+\frac{1}{3}\times\frac{1}{4}\)
Cách 1 = \(\frac{1}{3}\times\left(\frac{1}{2}+\frac{1}{4}\right)\) Cách 2 =\(\frac{1}{6}+\frac{1}{12}\)
= \(\frac{1}{3}\times\frac{3}{4}\) =\(\frac{1}{4}\)
=\(\frac{1}{4}\)
b. \(\left(\frac{3}{4}+\frac{1}{2}\right)\times2\)
Cách 1 =\(\frac{5}{4}\times2\) Cách 2 =\(\frac{3}{4}\times2+\frac{1}{2}\times2\)
=\(\frac{5}{2}\) =\(\frac{3}{2}+1\)
=\(\frac{5}{2}\)
c. \(\frac{1}{2}\times\frac{1}{3}-\frac{1}{3}\times\frac{1}{4}\)
C1 =\(\frac{1}{3}\times\left(\frac{1}{2}-\frac{1}{4}\right)\) C2 =\(\frac{1}{6}-\frac{1}{12}\)
=\(\frac{1}{3}\times\frac{1}{4}\) =\(\frac{1}{12}\)
=\(\frac{1}{12}\)
d. \(\left(\frac{4}{3}-\frac{1}{2}\right)\times\frac{2}{3}\)
C1 =\(\frac{5}{6}\times\frac{2}{3}\) C2 =\(\frac{4}{3}\times\frac{2}{3}-\frac{1}{2}\times\frac{2}{3}\)
=\(\frac{5}{9}\) =\(\frac{8}{9}-\frac{2}{6}\)
=\(\frac{5}{9}\)
B1:Tính nhanh:
a)M= -1/3 . 141/17 - 39/3 . -1/17
b)N= -9/16 . 13/3 - (-3/4)^2 . 19/3
c)P=(1+1/1.3) (1+1/2.4) (1+1/3.5)......(1+1/99.101)
B2:Tìm x,biết
a)1/2+3/2:x=1/4
b)3/4+1/4.x=7
c)1/2.4 + 1/4.6 +.........+1/(2x-2).2x = 11/48
B3:Tìm x,biết
a)(x-1/2)^2=1/81
b)x+x(1+1/x)+x(1+2/x)=1/3
c)2/x+4=3/x+5
a, 3/2 x 4/5 - x = 2/3
b, x x 3 1/3 = 3 1/3 : 4 1/4
c,5 2/3 : x = 3 2/3 - 2 1/2
`@` `\text {Ans}`
`\downarrow`
`a,`
\(\dfrac{3}{2}\times\dfrac{4}{5}-x=\dfrac{2}{3}\)
\(\dfrac{6}{5}-x=\dfrac{2}{3}\)
\(x=\dfrac{6}{5}-\dfrac{2}{3}\)
\(x=\dfrac{8}{15}\)
Vậy, `x = \dfrac{8}{15}`
`b,`
\(x\times3\dfrac{1}{3}=3\dfrac{1}{3}\div4\dfrac{1}{4}\)
\(x\times3\dfrac{1}{3}=\dfrac{40}{51}\)
\(x=\dfrac{40}{51}\div3\dfrac{1}{3}\)
\(x=\dfrac{4}{17}\)
Vậy, `x=`\(\dfrac{4}{17}\)
`c,`
\(5\dfrac{2}{3}\div x=3\dfrac{2}{3}-2\dfrac{1}{2}\)
\(\dfrac{17}{3}\div x=\dfrac{7}{6}\)
\(x=\dfrac{17}{3}\div\dfrac{7}{6}\)
\(x=\dfrac{34}{7}\)
Vậy, `x=`\(\dfrac{34}{7}\)
a,\(\dfrac{3}{2}.\dfrac{4}{5}-x=\dfrac{2}{3}\)
\(\dfrac{4}{5}-x=\dfrac{2}{3}:\dfrac{3}{2}\)
\(\dfrac{4}{5}-x=\dfrac{4}{9}\)
\(x=\dfrac{4}{5}-\dfrac{4}{9}\)
\(x=\dfrac{16}{45}\)
b,\(x.3.\dfrac{1}{3}=\dfrac{31}{3}\div\dfrac{4}{14}\)
\(x.3.\dfrac{1}{3}=\dfrac{217}{6}\)
\(x.3=\dfrac{217}{6}\div\dfrac{1}{3}\)
\(x\div3=\dfrac{217}{2}\)
\(x=\dfrac{217}{2}\div3\)
\(x=\dfrac{217}{6}\)