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NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
30 tháng 11 2023
\(\dfrac{x-3}{5-x}\) = \(\dfrac{5}{7}\) (đk \(x\) ≠ 5)
7.(\(x\) - 3) = 5.(5 - \(x\))
7\(x\) - 21 = 25 - 5\(x\)
7\(x\) + 5\(x\) = 25 + 21
12\(x\) = 46
\(x\) = 46 : 12
\(x\) = \(\dfrac{23}{6}\)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
30 tháng 11 2023
\(\dfrac{\left|x-2\right|}{2}\) = \(\dfrac{\left|2x+3\right|}{3}\)
3.|\(x\) - 2| = |2\(x\) + 3|.2
lập bảng ta có:
| \(x\) | - \(\dfrac{3}{2}\) 2 |
| 3.|\(x\) -2| | -3\(x\) + 6 3\(x\) - 6 0 3\(x\) - 6 |
| |2\(x\) + 3|.2 | -4\(x\) - 6 0 -4\(x\) - 6 0 4\(x\) + 6 |
Theo bảng trên ta có:
\(x\) < - \(\dfrac{3}{2}\) ⇒ -3\(x\) + 6 = - 4\(x\) - 6
-\(3x\) + 4\(x\) = - 6 - 6
\(x\) = -12
- \(\dfrac{3}{2}\) < \(x\) < 2 ⇒ 3\(x\) - 6 = - 4\(x\) - 6
3\(x\) + 4\(x\) = 6 - 6
7\(x\) = 0
\(x\) = 0
2 < \(x\) ⇒ 3\(x\)- 6 = 4\(x\) + 6
4\(x\) - 3\(x\) = - 6 - 6
\(x\) = -12 (loại)
Vậy \(x\) \(\in\) {-12; 0}
26 tháng 10 2017
A=(\(\dfrac{1}{3}-\dfrac{1}{3}\))\(+\left(\dfrac{3}{5}+\left(\dfrac{-3}{5}\right)\right)+\left(\dfrac{-5}{7}+\dfrac{5}{7}\right)+\left(\dfrac{-7}{9}+\dfrac{7}{9}\right)\)\(+\left(\dfrac{-11}{13}-\dfrac{9}{11}\right)\)
A\(=0+0+0+0+\dfrac{-238}{143}\)
A\(=\dfrac{-238}{143}\)
\(B=\left(1+\dfrac{1}{2}\right)+\left(1+\dfrac{1}{4}\right)+\left(1+\dfrac{1}{8}\right)+\left(1+\dfrac{1}{32}\right)+\left(1+\dfrac{1}{64}\right)-7\)
\(B=\left(1+1+1+1+1\right)+\left(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}\right)-7\)
\(B=6+\dfrac{63}{64}-7\)
\(B=-1+\dfrac{63}{64}\)
\(B=\dfrac{-1}{64}\)
26 tháng 7 2023
1:
a: x/15=-2/6
=>x/15=-1/3
=>x=-5
b: 3/x=1,8/2
=>3/x=9/10
=>x=3*10/9=30/9=10/3
c: (x-3)/(x+2)=2/7
=>2x+4=7x-21
=>-5x=-25
=>x=5
d: (x+1)/3=(x-6)/8
=>8x+8=3x-18
=>5x=-26
=>x=-26/5
e: (2-x)/5=(x+4)/3
=>3(2-x)=5(x+4)
=>5x+20=6-3x
=>8x=-14
=>x=-7/4
g: (2x+1)/(-3)=(1-x)/2
=>2(2x+1)=3(x-1)
=>4x+2=3x-3
=>x=-5
1 tháng 10 2017
\(LINH=\dfrac{3}{1^2.2^2}+\dfrac{7}{3^2.4^2}+\dfrac{11}{5^2.6^2}+\dfrac{15}{7^2.8^2}+\dfrac{19}{9^2.10^2}\)
\(LINH=\dfrac{1+2}{1^2.2^2}+\dfrac{3+4}{3^2.4^2}+\dfrac{5+6}{5^2.6^2}+\dfrac{7+8}{7^2.8^2}+\dfrac{9+10}{9^2.10^2}\)
\(LINH=\dfrac{1}{1^2.2^2}+\dfrac{2}{1^2.2^2}+\dfrac{3}{3^2.4^2}+\dfrac{4}{3^2.4^2}+\dfrac{5}{5^2.6^2}+\dfrac{6}{5^2.6^2}+\dfrac{7}{7^2.8^2}+\dfrac{8}{7^2.8^2}+\dfrac{9}{9^2.10^2}+\dfrac{10}{9^2.10^2}\)
\(LINH=\dfrac{1}{1.2^2}+\dfrac{1}{1^2.2}+\dfrac{1}{3.4^2}+\dfrac{1}{3^2.4}+\dfrac{1}{5.6^2}+\dfrac{1}{5^2.6}+\dfrac{1}{7.8^2}+\dfrac{1}{7^2.8}+\dfrac{1}{9.10^2}+\dfrac{1}{9^2.10}\)\(LINH=\dfrac{1}{4}+\dfrac{1}{2}+\dfrac{1}{48}+\dfrac{1}{36}+\dfrac{1}{180}+\dfrac{1}{150}+\dfrac{1}{448}+\dfrac{1}{392}+\dfrac{1}{900}+\dfrac{1}{810}\)Vì:
\(\left\{{}\begin{matrix}\dfrac{1}{48}< \dfrac{1}{32}\\\dfrac{1}{36}< \dfrac{1}{32}\\...............\\\dfrac{1}{810}< \dfrac{1}{32}\end{matrix}\right.\)
Nên:
\(\dfrac{1}{48}+\dfrac{1}{36}+.....+\dfrac{1}{810}< \dfrac{1}{32}+\dfrac{1}{32}+....+\dfrac{1}{32}\)
\(\Rightarrow\dfrac{1}{48}+\dfrac{1}{36}+....+\dfrac{1}{810}< \dfrac{1}{32}.8=\dfrac{1}{4}\)
Nên:
\(LINH=\dfrac{1}{4}+\dfrac{1}{2}+\dfrac{1}{48}+\dfrac{1}{36}+....+\dfrac{1}{810}< \dfrac{1}{4}+\dfrac{1}{2}+\dfrac{1}{4}=1\)
Nên \(LINH< 1\left(đpcm\right)\)
28 tháng 5 2022
Sửa đề: \(M=\dfrac{\left(\dfrac{3}{10}-\dfrac{4}{15}-\dfrac{7}{20}\right)\cdot\dfrac{5}{19}}{\left(\dfrac{1}{5}+\dfrac{1}{7}-\dfrac{-3}{35}\right)\cdot\dfrac{-4}{45}}\)
\(=\dfrac{\dfrac{3\cdot6-4\cdot4-7\cdot3}{60}\cdot\dfrac{5}{19}}{\dfrac{7+5+3}{35}\cdot\dfrac{-4}{45}}=\dfrac{\dfrac{-19}{60}\cdot\dfrac{5}{19}}{\dfrac{15}{35}\cdot\dfrac{-4}{45}}=\dfrac{-1}{12}:\dfrac{-4}{105}=\dfrac{105}{60}=\dfrac{7}{4}\)
26 tháng 5 2022
a: 2x(x-1/7)=0
=>x(x-1/7)=0
=>x=0 hoặc x=1/7
b: \(\dfrac{3}{4}+\dfrac{1}{4}:x=\dfrac{2}{5}\)
\(\Leftrightarrow\dfrac{1}{4}:x=\dfrac{2}{5}-\dfrac{3}{4}=\dfrac{8}{20}-\dfrac{15}{20}=\dfrac{-7}{20}\)
nên \(x=\dfrac{-1}{4}:\dfrac{7}{20}=\dfrac{-20}{4\cdot7}=\dfrac{-5}{7}\)
c: \(\Leftrightarrow\dfrac{41}{9}:\dfrac{41}{18}-7< x< \left(3.2:3.2+\dfrac{45}{10}\cdot\dfrac{31}{45}\right):\left(-21.5\right)\)
\(\Leftrightarrow2-7< x< \dfrac{\left(1+3.1\right)}{-21.5}\)
\(\Leftrightarrow-5< x< \dfrac{-41}{215}\)
mà x là số nguyên
nên \(x\in\left\{-4;-3;-2;-1\right\}\)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
10 tháng 7 2023
\(\dfrac{3}{5}\)\(x\) - \(\dfrac{11}{5}\) = \(\dfrac{-3}{14}\) : \(\dfrac{5}{7}\)
\(\dfrac{3}{5}\)\(x\) - \(\dfrac{11}{5}\) = - \(\dfrac{3}{10}\)
\(\dfrac{3}{5}\)\(x\) = - \(\dfrac{3}{10}\) + \(\dfrac{11}{5}\)
\(\dfrac{3}{5}\)\(x\) = \(\dfrac{19}{10}\)
\(x\) = \(\dfrac{19}{10}\) : \(\dfrac{3}{5}\)
\(x\) = \(\dfrac{19}{6}\)
H9
HT.Phong (9A5)
CTVHS
10 tháng 7 2023
\(\dfrac{3}{5}x-\dfrac{11}{5}=-\dfrac{3}{14}:\dfrac{5}{7}\)
\(\Rightarrow\dfrac{3}{5}x-\dfrac{11}{5}=-\dfrac{3}{14}\cdot\dfrac{7}{5}\)
\(\Rightarrow\dfrac{3}{5}x-\dfrac{11}{5}=-\dfrac{3}{10}\)
\(\Rightarrow\dfrac{3}{5}x=-\dfrac{3}{10}+\dfrac{11}{5}\)
\(\Rightarrow\dfrac{3}{5}x=\dfrac{19}{10}\)
\(\Rightarrow x=\dfrac{19}{10}:\dfrac{3}{5}\)
\(\Rightarrow x=\dfrac{19}{6}\)
huhuuu
k