a. x : 1/6 = 3
b. 3/7 + x = 2/7 + 1
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27 tháng 6 2023
a: \(\dfrac{7}{x}-\dfrac{2}{6}-2>\dfrac{2\left(x+1\right)}{3}\)
=>\(\dfrac{7}{x}>\dfrac{2x+2}{3}+\dfrac{1}{3}+2=\dfrac{2x+2+1+6}{3}=\dfrac{2x+9}{3}\)
=>\(\dfrac{7}{x}-\dfrac{2x+9}{3}>0\)
=>\(\dfrac{21-2x^2-9x}{3x}>0\)
=>\(\dfrac{2x^2+9x-21}{x}< 0\)
TH1: x>0 và 2x^2+9x-21<0
=>x>0 và \(\dfrac{-9-\sqrt{249}}{4}< x< \dfrac{-9+\sqrt{249}}{4}\)
=>\(0< x< \dfrac{-9+\sqrt{249}}{4}\)
TH2: x<0 và 2x^2+9x-21>0
=>x<0 và (x<-9-căn 249)/4 hoặc (x>(-9+căn 249)/4))
=>x<(-9-căn 249)/4
TG
3 tháng 4 2022
a,C1
(5/6 + 5/8) x 2/3
= 35/24 x 2/3
=35/36
C2
(5/6 + 5/8) x 2/3
= 5/6x2/3 + 5/8x2/3
= 10/18 + 10/24
= 35/36
b,C1
7/5 x 3/4 - 1/2 x 3/4
= 21/20 - 3/8
= 27/40
C2
7/5 x 3/4 - 1/2 x 3/4
=3/4 x (7/5-1/2)
=3/4x9/10
=27/40
TG
3 tháng 4 2022
a, 5/6 x (1/8x2/3)
=5/6 x 1/12
=5/72
b,(7/5 - 1/2) x 3/4
=0,9 x 3/4
=3,06
c,(5/6+5/8) x 2/3
=70/48 x 2/3
=35/36
CK
3 tháng 4 2022
a, 5/6 x (1/8x2/3)
=5/6 x 1/12
=5/72
b,(7/5 - 1/2) x 3/4
=0,9 x 3/4
=3,06
c,(5/6+5/8) x 2/3
=70/48 x 2/3
=35/36
12 tháng 5 2023
3:
a: =>x=0 hoặc x+5=0
=>x=0 hoặc x=-5
b: =>x^2=4
=>x=2 hoặc x=-2
c: =>(x-5)(2x+1+x+6)=0
=>(x-5)(3x+7)=0
=>x=5 hoặc x=-7/3
MP
12 tháng 5 2023
1.
a. 2x - 6 > 0
\(\Leftrightarrow\) 2x > 6
\(\Leftrightarrow\) x > 3
S = \(\left\{x\uparrow x>3\right\}\)
b. -3x + 9 > 0
\(\Leftrightarrow\) - 3x > - 9
\(\Leftrightarrow\) x < 3
S = \(\left\{x\uparrow x< 3\right\}\)
c. 3(x - 1) + 5 > (x - 1) + 3
\(\Leftrightarrow\) 3x - 3 + 5 > x - 1 + 3
\(\Leftrightarrow\) 3x - 3 + 5 - x + 1 - 3 > 0
\(\Leftrightarrow\) 2x > 0
\(\Leftrightarrow\) x > 0
S = \(\left\{x\uparrow x>0\right\}\)
d. \(\dfrac{x}{3}-\dfrac{1}{2}>\dfrac{x}{6}\)
\(\Leftrightarrow\dfrac{2x}{6}-\dfrac{3}{6}>\dfrac{x}{6}\)
\(\Leftrightarrow2x-3>x\)
\(\Leftrightarrow2x-3-x>0\)
\(\Leftrightarrow x-3>0\)
\(\Leftrightarrow x>3\)
\(S=\left\{x\uparrow x>3\right\}\)
2.
a.
Ta có: a > b
3a > 3b (nhân cả 2 vế cho 3)
3a + 7 > 3b + 7 (cộng cả 2 vế cho 7)
b. Ta có: a > b
a > b (nhân cả 2 vế cho 1)
a + 3 > b + 3 (cộng cả 2 vế cho 3) (1)
Ta có; 3 > 1
b + 3 > b + 1 (nhân cả 2 vế cho 1b) (2)
Từ (1) và (2) \(\Rightarrow\) a + 3 > b + 1
c.
5a - 1 + 1 > 5b - 1 + 1 (cộng cả 2 vế cho 1)
5a . \(\dfrac{1}{5}\) > 5b . \(\dfrac{1}{5}\) (nhân cả 2 vế cho \(\dfrac{1}{5}\) )
a > b
3.
a. 2x(x + 5) = 0
\(\Leftrightarrow\left[{}\begin{matrix}2x=0\\x+5=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-5\end{matrix}\right.\)
\(S=\left\{0,-5\right\}\)
b. x2 - 4 = 0
\(\Leftrightarrow x\left(x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\end{matrix}\right.\)
\(S=\left\{0,4\right\}\)
d. (x - 5)(2x + 1) + (x - 5)(x + 6) = 0
\(\Leftrightarrow\left(x-5\right)\left(2x+1+x+6\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(3x+7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\3x+7=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=\dfrac{-7}{3}\end{matrix}\right.\)
\(S=\left\{5,\dfrac{-7}{3}\right\}\)
7 tháng 7 2021
Giải:
a) \(2\dfrac{17}{20}-1\dfrac{15}{11}+6\dfrac{9}{20}:3\)
\(=\dfrac{57}{20}-\dfrac{26}{11}+\dfrac{129}{20}:3\)
\(=\dfrac{107}{220}+\dfrac{43}{20}\)
\(=\dfrac{29}{11}\)
b) \(4\dfrac{3}{7}:\left(\dfrac{7}{5}.4\dfrac{3}{7}\right)\)
\(=\dfrac{31}{7}:\left(\dfrac{7}{5}.\dfrac{31}{7}\right)\)
\(=\dfrac{31}{7}:\dfrac{31}{5}\)
\(=\dfrac{5}{7}\)
c) \(\left(3\dfrac{2}{9}.\dfrac{15}{23}.1\dfrac{7}{29}\right):\dfrac{5}{23}\)
\(=\left(\dfrac{29}{9}.\dfrac{15}{23}.\dfrac{36}{29}\right):\dfrac{5}{23}\)
\(=\dfrac{60}{23}:\dfrac{5}{23}\)
\(=12\)
DN
4
LT
15 tháng 4 2021
a) \(\dfrac{3}{5}+x=\dfrac{4}{3}\)
\(\Leftrightarrow x=\dfrac{4}{3}-\dfrac{3}{5}\)
\(\Leftrightarrow x=\dfrac{20}{15}-\dfrac{9}{15}\)
\(\Leftrightarrow x=\dfrac{11}{15}\)
b) \(x+\dfrac{5}{6}=\dfrac{1}{7}\)
\(\Leftrightarrow x=\dfrac{1}{7}-\dfrac{5}{6}\)
\(\Leftrightarrow x=\dfrac{6}{42}-\dfrac{35}{42}\)
\(\Leftrightarrow x=-\dfrac{29}{42}\)
c) \(x\times\dfrac{3}{8}=\dfrac{3}{4}\)
\(\Leftrightarrow x=\dfrac{3}{4}:\dfrac{3}{8}\)
\(\Leftrightarrow x=\dfrac{3}{4}\times\dfrac{8}{3}\)
\(\Leftrightarrow x=2\)
d) \(\dfrac{4}{5}\times x=\dfrac{3}{7}\)
\(\Leftrightarrow x=\dfrac{3}{7}:\dfrac{4}{5}\)
\(\Leftrightarrow x=\dfrac{3}{7}\times\dfrac{5}{4}\)
\(\Leftrightarrow x=\dfrac{15}{28}\)
15 tháng 4 2021
a, \(\dfrac{3}{5}+x=\dfrac{4}{3}\Leftrightarrow x=\dfrac{4}{3}-\dfrac{3}{5}=\dfrac{20-9}{15}=\dfrac{11}{15}\)
b, \(x+\dfrac{5}{6}=\dfrac{1}{7}\Leftrightarrow x=\dfrac{1}{7}-\dfrac{5}{6}=\dfrac{6-35}{42}=\dfrac{-29}{42}\)
c, \(\dfrac{3x}{8}=\dfrac{3}{4}\Leftrightarrow\dfrac{3x}{8}=\dfrac{6}{8}\Rightarrow3x=6\Leftrightarrow x=2\)
d, \(\dfrac{4x}{5}=\dfrac{3}{7}\Leftrightarrow\dfrac{28x}{35}=\dfrac{15}{35}\Rightarrow x=\dfrac{15}{28}\)
a) x : 1/6 = 3
x = 3 x 1/6
x = 1/2
b) 3/7 + x = 2/7 + 1
3/7 + x = 9/7
x = 9/7 - 3/7
x = 6/7
\(x:\dfrac{1}{6}=3\)
\(x=\dfrac{1}{6}\times3=\dfrac{3}{6}=\dfrac{1}{2}\)
\(\dfrac{3}{7}+x=\dfrac{2}{7}+1\)
\(\dfrac{3}{7}+x=\dfrac{2}{7}+\dfrac{1}{1}=\dfrac{2}{7}+\dfrac{7}{7}=\dfrac{9}{7}\)
\(x=\dfrac{9}{7}-\dfrac{3}{7}=\dfrac{6}{7}\)