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\(\left\{\dfrac{-5< 0< -0,4}{x\in Z}\right\}\Rightarrow x\in\left\{-4;-3;-2;-1\right\}\)
1.Tính
a.\(\dfrac{7}{23}\left[(-\dfrac{8}{6})-\dfrac{45}{18}\right]=\dfrac{7}{23}.-\dfrac{12}{6}=-\dfrac{7}{6}\)
b.\(\dfrac{1}{5}\div\dfrac{1}{10}-\dfrac{1}{3}(\dfrac{6}{5}-\dfrac{9}{4})=2-(-\dfrac{7}{20})=\dfrac{47}{20}\)
c.\(\dfrac{3}{5}.(-\dfrac{8}{3})-\dfrac{3}{5}\div(-6)=-\dfrac{3}{2}\)
d.\(\dfrac{1}{2}.(\dfrac{4}{3}+\dfrac{2}{5})-\dfrac{3}{4}.(\dfrac{8}{9}+\dfrac{16}{3})=-\dfrac{19}{5}\)
e.\(\dfrac{6}{7}\div(\dfrac{3}{26}-\dfrac{3}{13})+\dfrac{6}{7}.(\dfrac{1}{10}-\dfrac{8}{5})=-\dfrac{61}{7}\)
Bài 2
a.\(1^2_5x+\dfrac{3}{7}=\dfrac{4}{5}\)
\(x=\dfrac{13}{49}\)
b.\(\left|x-1,5\right|=2\)
Xảy ra 2 trường hợp
TH1
\(x-1,5=2\)
\(x=3,5\)
TH2
\(x-1,5=-2\)
\(x=-0,5\)
Vậy \(x=3,5\) hoặc \(x=-0,5\) .
Ngại làm quá trời ơi,lần sau bn tách ra nhá làm vậy mỏi tay quá.
b: \(\left(\dfrac{2}{5}-\dfrac{7}{10}x\right):\dfrac{5}{3}=-\dfrac{3}{4}\)
\(\Leftrightarrow\dfrac{2}{5}-\dfrac{7}{10}x=\dfrac{-3}{4}\cdot\dfrac{5}{3}=\dfrac{-5}{4}\)
\(\Leftrightarrow x\cdot\dfrac{7}{10}=\dfrac{2}{5}+\dfrac{5}{4}=\dfrac{8+25}{20}=\dfrac{33}{20}\)
\(\Leftrightarrow x=\dfrac{33}{20}:\dfrac{7}{10}=\dfrac{33}{20}\cdot\dfrac{10}{7}=\dfrac{33}{14}\)
c: \(\dfrac{7}{16}:\left(\dfrac{1}{4}x+\dfrac{9}{2}\right)-\dfrac{11}{6}=0\)
\(\Leftrightarrow\dfrac{7}{16}:\left(\dfrac{1}{4}x+\dfrac{9}{2}\right)=\dfrac{11}{6}\)
\(\Leftrightarrow x\cdot\dfrac{1}{4}+\dfrac{9}{2}=\dfrac{11}{6}:\dfrac{7}{16}=\dfrac{88}{21}\)
\(\Leftrightarrow x\cdot\dfrac{1}{4}=\dfrac{88}{21}-\dfrac{9}{2}=-\dfrac{13}{42}\)
hay \(x=-\dfrac{26}{21}\)
a: \(\Leftrightarrow-\dfrac{23}{5}\cdot\dfrac{50}{23}< x< \dfrac{-13}{5}:\dfrac{21}{15}=\dfrac{-13}{5}\cdot\dfrac{5}{7}=\dfrac{-13}{7}\)
=>-10<x<-13/7
hay \(x\in\left\{-9;-8;-7;-6;-5;-4;-3;-2\right\}\)
b: \(\Leftrightarrow-\dfrac{13}{3}\cdot\dfrac{1}{3}< x< \dfrac{-2}{3}\cdot\dfrac{4-3-9}{12}\)
\(\Leftrightarrow-\dfrac{13}{9}< x< \dfrac{4}{9}\)
mà x là số nguyên
nên \(x\in\left\{-1;0\right\}\)
a: Gọi số nguyên cần tìm là x
Theo đề, ta có: \(\dfrac{1}{3}+\left(\dfrac{2}{4}-1\dfrac{2}{5}\right)< x< 2\dfrac{1}{7}+\left(\dfrac{-2}{5}-\dfrac{1}{4}\right)\)
\(\Leftrightarrow\dfrac{1}{3}+\dfrac{1}{2}-\dfrac{7}{5}< x< \dfrac{15}{7}-\dfrac{2}{5}-\dfrac{1}{4}\)
\(\Leftrightarrow\dfrac{20}{60}+\dfrac{30}{60}-\dfrac{84}{60}< x< \dfrac{15\cdot20-2\cdot28-35}{140}\)
\(\Leftrightarrow-\dfrac{34}{60}< x< \dfrac{209}{140}\)
mà x là số nguyên
nên \(x\in\left\{0;1\right\}\)
b: Gọi số nguyên cần tìm là x
Theo đề, ta có: \(\dfrac{7}{3}+\dfrac{3}{4}-\dfrac{1}{5}>x>\dfrac{2}{3}-\dfrac{1}{4}+\dfrac{2}{7}\)
\(\Leftrightarrow\dfrac{7\cdot20+3\cdot15-12}{60}>x>\dfrac{56-21+2\cdot12}{84}\)
\(\Leftrightarrow\dfrac{173}{60}>x>\dfrac{59}{84}\)
mà x là số nguên
nên \(x\in\left\{2;1\right\}\)
\(\dfrac{1}{2}-\left(\dfrac{1}{3}+\dfrac{1}{4}\right)< ...........< \dfrac{1}{48}-\left(\dfrac{1}{16}-\dfrac{1}{6}\right)\)
\(\dfrac{-1}{12}< .........< \dfrac{1}{8}\)và số ghi trong ô trống là số nguyên nên số đó phải là 0 .
a: \(=\left|\dfrac{3}{2}-\dfrac{7}{3}\right|^2+\dfrac{1}{4}=\dfrac{17}{18}\)
b: \(=\left|1-2-\dfrac{1}{3}\right|+\dfrac{5}{6}=1+\dfrac{1}{3}+\dfrac{5}{6}=\dfrac{13}{6}\)
c: \(=\left|\dfrac{3}{2}-\dfrac{7}{4}\right|-\dfrac{7}{4}=-\dfrac{3}{2}\)
d: =x-5+8-x=3
5a.
\(\dfrac{1}{1.3}+\dfrac{1}{3.5}+....+\dfrac{1}{19.21}\\ =\dfrac{1}{2}\left(\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+....+\dfrac{1}{19}-\dfrac{1}{21}\right)\\ =\dfrac{1}{2}\left(1-\dfrac{1}{21}\right)\\ =\dfrac{1}{2}.\dfrac{20}{21}=\dfrac{10}{21}\)
b.
\(\dfrac{1}{1.3}+\dfrac{1}{3.5}+...+\dfrac{1}{\left(2n-1\right)\left(2n+1\right)}\\ =\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+....+\dfrac{1}{2n-1}-\dfrac{1}{2n+1}\right)\\ =\dfrac{1}{2}\left(1-\dfrac{1}{2n+1}\right)< \dfrac{1}{2}.1=\dfrac{1}{2}\)
a)\(3\dfrac{1}{3}:2\dfrac{1}{2}-1< x< 7\dfrac{2}{3}.\dfrac{3}{7}+\dfrac{5}{2}\)
\(\dfrac{4}{3}-1< x< \dfrac{23}{7}+\dfrac{5}{2}\)
\(\dfrac{1}{3}< x< \dfrac{81}{14}\)
Vì\(\dfrac{1}{3}=0,333333333333333333333333...\)
\(\dfrac{81}{14}=5,785714286\)
=>\(x=\left\{1;2;3;4;5\right\}\)
b)\(\dfrac{1}{2}-\left(\dfrac{1}{3}+\dfrac{1}{4}\right)< x< \dfrac{1}{48}-\left(\dfrac{1}{16}-\dfrac{1}{6}\right)\)
\(\dfrac{1}{2}-\dfrac{7}{12}< x< \dfrac{1}{48}+\dfrac{5}{48}\)
\(-\dfrac{1}{12}< x< \dfrac{1}{8}\)
Vì\(-\dfrac{1}{12}=-0.08333333333333333\)
\(\dfrac{1}{8}=0.125\)
=> \(x=\left\{0\right\}\)
a.\(3\dfrac{1}{3}:2\dfrac{1}{2}-1< x< 7\dfrac{2}{3}.\dfrac{3}{7}+\dfrac{5}{2}\)
\(\dfrac{4}{3}-1< x< \dfrac{23}{7}+\dfrac{5}{2}\)
\(\dfrac{1}{3}< x< \dfrac{81}{14}\)
\(0,3333...< x< 5,7857...\)
Vì \(x\in Z\Rightarrow x\in\left\{1;2;3;4;5\right\}\)
Vậy........
b. \(\dfrac{1}{2}-\left(\dfrac{1}{3}+\dfrac{1}{4}\right)< x< \dfrac{1}{48}-\left(\dfrac{1}{16}-\dfrac{1}{6}\right)\)
\(\dfrac{-1}{12}< x< \dfrac{1}{8}\)
\(-0,0833...< x< 0,125\)
Vì \(x\in Z\Rightarrow x\in\left\{0\right\}\)
Vậy............