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\(\frac{x}{2}=\frac{y}{3};\frac{y}{4}=\frac{z}{5}\)và x + y -z = 10
\(\frac{x}{2}=\frac{y}{3}=\frac{1}{4}.\frac{x}{2}=\frac{1}{4}.\frac{y}{3}\)\(=\frac{x}{8}=\frac{y}{12}\)
\(\frac{y}{4}=\frac{z}{5}=\frac{1}{3}.\frac{y}{4}=\frac{1}{3}.\frac{z}{5}=\frac{y}{12}=\frac{z}{15}\)
\(\Leftrightarrow\frac{x}{8}=\frac{y}{12}=\frac{z}{15}\)và x + y - z = 10
Theo tính chất dãy tỉ số bằng nhau:
\(\frac{x}{8}=\frac{y}{12}=\frac{z}{15}=\frac{x+y-z}{8+12-15}=\frac{10}{5}=2\)
* \(\frac{x}{8}=2\Rightarrow x=2.8=16\)
* \(\frac{y}{12}=2\Rightarrow y=2.12=24\)
* \(\frac{z}{5}=2\Rightarrow z=2.5=10\)
Vậy...
Ý mk nhầm chút xíu nhé! Cko sorry!
* \(\frac{z}{15}=2\Rightarrow z=2.15=30\)
... :( Xl
Ta có:
(-3/2:3/-4)*(-9/2)-1/4<x/8<-1/2:3/4:1/8+1
Xét VT = (-3/2.-4/3).(-9/2)-1/4
= 2.-9/2-1/4
=-9-1/4=-37/4=--222/24
Xét VP = -1/2:3/4:1/8+1
=-1/2.4/3.8+1
=-16/3+1
=-13/3=-104/24
=>-222/24<x/8<-104/24=>-222/24<x.3/24<-104/24=>-222<x.3<-104
=>x.3={-221;-220;...;--105}Mà x.3 chia hết cho 3=>x.3 thuộc{-219;-216;...;-105}
=>x={-73;-72;.....-35}
Vậy ..........
B1:
a) \(\frac{x+4}{x+3}=\frac{x+9}{x+4}\)
-->(x+4)(x+4)=(x+3)(x+9)
\(x^2\)+4x+4x+16=\(x^2\)+9x+3x+27
\(x^2-x^2\)+4x+4x-9x-3x= - 16+27
- 4x=11
x=\(\frac{-4}{11}\)
b) \(\frac{x-5}{x+3}=\frac{x-4}{x+6}\)
-->(x-5)(x+6)=(x+3)(x-4)
\(x^2\)+6x-5x-30=\(x^2\)-4x+3x-12
\(x^2-x^2\)+6x-5x+4x-3x=30-12
2x=18
x=9
c)\(\frac{3x-1}{3x}=\frac{2x-1}{2x+1}\)
--> (3x-1)(2x+1)=3x.(2x-1)
\(6x^2\)+3x-2x-1=\(6x^2\)-3x
\(6x^2-6x^2\)+3x-2x+3x=1
4x=1
x=\(\frac{1}{4}\)
a) \(\frac{x-3}{x+5}=\frac{5}{7}\)
\(\Rightarrow\left(x-3\right).7=\left(x+5\right).5\)
\(\Rightarrow7x-21=5x+25\)
\(\Rightarrow7x-5x=21+25\)
\(\Rightarrow2x=46\)
\(\Rightarrow x=23\)
Vậy \(x=23\)
b) \(\frac{7}{x-1}=\frac{x+1}{9}\)
\(\Rightarrow\left(x-1\right).\left(x+1\right)=7.9\)
\(\Rightarrow\left(x-1\right)x-\left(x+1\right)=7.9\)
\(\Rightarrow x^2-x-x-1=63\)
\(\Rightarrow x^2-1=63\)
\(\Rightarrow x^2=64\)
\(\Rightarrow x=8\) hoặc \(x=-8\)
Vậy \(x=8\) hoặc \(x=-8\)
c) \(\frac{x+4}{20}=\frac{5}{x+4}\)
\(\Rightarrow\left(x+4\right)^2=100\)
\(\Rightarrow x+4=\pm10\)
+) \(x+4=10\Rightarrow x=6\)
+) \(x+4=-10\Rightarrow x=-16\)
Vậy \(x\in\left\{6;-16\right\}\)
\(\frac{2}{3}x+\frac{5}{7}=\frac{3}{10}\)
\(\Rightarrow\frac{2}{3}x=\frac{3}{10}-\frac{5}{7}\)
\(\Rightarrow\frac{2}{3}x=-\frac{29}{70}\)
\(\Rightarrow x=-\frac{29}{70}:\frac{2}{3}\)
\(\Rightarrow x=-\frac{87}{140}\)
tíc mình nha
a. 6,5 -9/4:/x+1/3\=/-2\
6,5-9/4:/x+1/3\=2
9/4:/x+1/3\=6,5-2
9/4:/x+1/3\=4,5
/x+1/3\=9/4:4,5
/x+1/3\=1/2
x+1/3=1/2 hoặc x+1/3= -1/2
x= 1/2-1/3 x= -1/2-1/3
x= 1/6 x= -5/6
Vậy x=1/6 hoặcx= -5/6
b. 2-/3/2x-1/4\ = /-5/4\
2-/3/2x-1/4\=5/4
/3/2x-1/4\=2-5/4
/3/2x-1/4\=3/4
3/2x-1/4=3/4 hoặc 3/2x-1/4= -3/4
3/2x=3/4+1/4 3/2x= -3/4+1/4
3/2x=1 3/2x= -1/2
x=1:3/2 x= -1/2:3/2
x=2/3 x= -1/3
Vậy x=2/3 hoặc x= -1/3
3/4+1/4:x=2/5
1/4:x=2/5-3/4
1/4:x=-7/20
x=1/4:-7/20
x=-5/7
3/4+1/4:x=2/5
1/4:x=2/5-3/4
1/4:x=-7/20
x=1/4:(-7/20)
x=-5/7