\(\dfrac{-29}{12}+1+\dfrac{19}{-12}\)\(\le\)x\(\le\dfrac{-1}{3}+\dfrac{3}{4}+\dfrac{7}{12}\)
\(\dfrac{-5}{3}+1+\dfrac{1}{-3}\le x\le\dfrac{8}{10}+\dfrac{1}{5}+2\)
a)x=\(\dfrac{1}{4}+\dfrac{2}{13}\)
b)\(\dfrac{x}{3}=\dfrac{2}{3}+\dfrac{-1}{7}\)
c)\(\dfrac{-8}{3}+\dfrac{-1}{3}\le x\le\dfrac{-2}{7}+\dfrac{-5}{7}\)
d)\(\dfrac{-5}{6}+\dfrac{8}{3}\dfrac{29}{-x}\le x\le\dfrac{-1}{2}+2+\dfrac{5}{2}\)
[1] Cho các tập hợp A = [ -5; \(\dfrac{1}{2}\) ]; B = ( -3; \(+\infty\) ). Khi đó tập hợp \(A\cap B\) bằng:
A. { x ∈ R | -3 \(\le x\le\dfrac{1}{2}\) } B. { x ∈ R | - 3 < x \(\le\dfrac{1}{2}\) } C. { x ∈ R | -5 < x \(\le\dfrac{1}{2}\) } D. { x ∈ R | -3 \(\le x< \dfrac{1}{2}\)}
Ta có:
Tập hợp A:
\(A=\left[-5;\dfrac{1}{2}\right]\)
Tập hợp B:
\(B=\left(-3;+\infty\right)\)
Mà: \(A\cap B\)
\(\Rightarrow\left\{x\in R|-3\le x\le\dfrac{1}{2}\right\}\)
⇒ Chọn A
a. \(-4\dfrac{3}{5}\times2\dfrac{4}{23}\le x\le-2\dfrac{3}{5}\times1\dfrac{6}{15}\)
\(-4\dfrac{3}{5}\cdot2\dfrac{4}{23}\le x\le-2\dfrac{3}{5}\cdot1\dfrac{6}{15}\)
\(\Leftrightarrow-10\le x\le-\dfrac{91}{25}\)
\(\Leftrightarrow x\in\left\{-9;-8;-7;-6;-5;-4\right\}\)
\(\Rightarrow-\dfrac{23}{5}\cdot\dfrac{50}{23}\le x\le-\dfrac{13}{5}\cdot\dfrac{7}{5}\\ \Rightarrow-10\le x\le-\dfrac{91}{25}\\ \Rightarrow-\dfrac{2500}{25}\le x\le-\dfrac{91}{25}\\ \Rightarrow x\in\left\{-\dfrac{2499}{25};-\dfrac{2498}{25};...;-\dfrac{92}{25};-\dfrac{91}{25}\right\}\)
Tìm số nguyên x biết: a) \(-4\dfrac{3}{5}.2\dfrac{4}{23}\le x\le-2\dfrac{3}{5}:1\dfrac{6}{15}\)
b)\(-4\dfrac{1}{3}.\left(\dfrac{1}{2}-\dfrac{1}{6}\right)\le x\le-\dfrac{2}{3}\left(\dfrac{1}{3}-\dfrac{1}{2}-\dfrac{3}{4}\right)\)
a: \(\Leftrightarrow-\dfrac{23}{5}\cdot\dfrac{50}{23}< =x< =\dfrac{-13}{5}:\dfrac{21}{15}\)
=>-10<=x<=-13/7
hay \(x\in\left\{-10;-9;...;-2\right\}\)
b: \(\Leftrightarrow-\dfrac{13}{3}\cdot\dfrac{1}{3}< =x< =-\dfrac{2}{3}\cdot\dfrac{-11}{12}\)
=>-13/9<=x<=11/18
hay \(x\in\left\{-1;0\right\}\)
Tìm x: \(3\dfrac{2}{3}.\left(\dfrac{1}{5}-\dfrac{1}{2}\right)\le x\le\dfrac{3}{11}.\left(\dfrac{1}{5}+\dfrac{1}{3}+\dfrac{1}{2}\right)\)
Sửa đề: Tìm số nguyên x:
\(3\dfrac{2}{3}.\left(\dfrac{1}{5}-\dfrac{1}{2}\right)\le x\le\dfrac{3}{11}.\left(\dfrac{1}{5}+\dfrac{1}{3}+\dfrac{1}{2}\right)\)
\(\Rightarrow\dfrac{11}{3}.\dfrac{-3}{10}\le x\le\dfrac{3}{11}.\dfrac{31}{30}\)
\(\Rightarrow-\dfrac{11}{10}\le x\le\dfrac{31}{110}\)
Vì \(x\in Z\) nên \(x\in\left\{-1;0\right\}\)
Vậy..............
Chúc bạn học tốt!!!
So sánh \(\dfrac{9}{170};\dfrac{9}{230};\dfrac{53}{144}\)
Số nguyên \(x\) thỏa mãn \(\left(\dfrac{3}{4}-\dfrac{2}{3}\right)+\dfrac{5}{6}\le x\le\dfrac{4}{5}-\left(\dfrac{3}{10}-\dfrac{5}{4}\right)\)
A. \(x=1\) B. \(x=0\) C. \(x=2\) D. \(x\in\left\{0;1\right\}\)
EM CẦN GẤP Ạ!
BT3: Tìm x, biết:
7) \(\dfrac{-5}{17}+\dfrac{3}{17}\le\dfrac{x}{17}\le\dfrac{13}{17}+\dfrac{-11}{17}\)
8) \(\dfrac{2}{3}\left(\dfrac{1}{2}+\dfrac{3}{4}-\dfrac{1}{3}\right)\le\dfrac{x}{18}\le\dfrac{7}{3}\left(\dfrac{1}{2}-\dfrac{1}{6}\right)\)
7) \(\dfrac{-5}{17}+\dfrac{3}{17}\le\dfrac{x}{17}\le\dfrac{13}{17}+\dfrac{-11}{17}\)
\(\Rightarrow\dfrac{-2}{17}\le\dfrac{x}{17}\le\dfrac{2}{17}\)
\(\Rightarrow-2\le x\le2\)
\(\Rightarrow x\in\left\{-2;-1;0;1;2\right\}\)
8) \(\dfrac{2}{3}\left(\dfrac{1}{2}+\dfrac{3}{4}-\dfrac{1}{3}\right)\le\dfrac{x}{18}\le\dfrac{7}{3}\left(\dfrac{1}{2}-\dfrac{1}{6}\right)\)
\(\Rightarrow\dfrac{2}{3}\left(\dfrac{6}{12}+\dfrac{9}{12}-\dfrac{4}{12}\right)\le\dfrac{x}{18}\le\dfrac{7}{3}\left(\dfrac{6}{12}-\dfrac{2}{12}\right)\)
\(\Rightarrow\dfrac{2}{3}\cdot\dfrac{11}{12}\le\dfrac{x}{18}\le\dfrac{7}{3}\cdot\dfrac{4}{12}\)
\(\Rightarrow\dfrac{22}{36}\le\dfrac{x}{18}\le\dfrac{28}{36}\)
\(\Rightarrow\dfrac{11}{18}\le\dfrac{x}{18}\le\dfrac{14}{18}\)
\(\Rightarrow x\in\left\{11;12;13;14\right\}\)
8) \(\dfrac{2}{3}\left(\dfrac{1}{2}+\dfrac{3}{4}-\dfrac{1}{3}\right)\le\dfrac{x}{18}\le\dfrac{7}{3}\left(\dfrac{1}{2}-\dfrac{1}{6}\right)\\ \dfrac{2}{3}\left(\dfrac{6}{12}+\dfrac{9}{12}-\dfrac{4}{12}\right)\le\dfrac{x}{18}\le\dfrac{7}{3}\left(\dfrac{3}{6}-\dfrac{1}{6}\right)\\ \dfrac{2}{3}.\dfrac{11}{12}\le\dfrac{x}{18}\le\dfrac{7}{3}.\dfrac{2}{6}\\ \dfrac{11}{18}\le\dfrac{x}{18}\le\dfrac{14}{18}\\ \Rightarrow11\le x\le14\\ \Rightarrow x\in\left\{11;12;13;14\right\}\)
7) \(\dfrac{-5}{17}+\dfrac{3}{17}\le\dfrac{x}{17}\le\dfrac{13}{17}+\dfrac{-11}{17}\\ \dfrac{-2}{17}\le\dfrac{x}{17}\le\dfrac{2}{17}\\ \Rightarrow-2\le x\le2\\ \Rightarrow x\in\left\{-2;-1;0;1;2\right\}\)
Giải các bất phương trình sau:
1) \(\dfrac{2x-5}{x^2-6x-7}\le\dfrac{1}{x-3}\)
2) \(\dfrac{\left(3-2x\right)x^2}{\left(x-1\right)}\ge0\)
3) \(\dfrac{2x}{x-1}\le\dfrac{5}{2x-1}\)
1.
ĐK: \(x\ne7;x\ne-1;x\ne3\)
\(\dfrac{2x-5}{x^2-6x-7}\le\dfrac{1}{x-3}\left(1\right)\)
TH1: \(x< -1\)
\(\left(1\right)\Leftrightarrow\left(2x-5\right)\left(x-3\right)\ge x^2-6x-7\)
\(\Leftrightarrow2x^2-11x+15\ge x^2-6x-7\)
\(\Leftrightarrow x^2-5x+22\ge0\)
\(\Leftrightarrow\) Bất phương trình đúng với mọi \(x< -1\)
TH2: \(-1< x< 3\)
\(\left(1\right)\Leftrightarrow\left(3-x\right)\left(2x-5\right)\ge\left(7-x\right)\left(x+1\right)\)
\(\Leftrightarrow-2x^2+11x-15\ge-x^2+6x+7\)
\(\Leftrightarrow-x^2+5x-22\ge0\)
\(\Rightarrow\) vô nghiệm
TH3: \(3< x< 7\)
Khi đó \(\dfrac{2x-5}{x^2-6x-7}\le0\); \(\dfrac{1}{x-3}>0\)
\(\Rightarrow\) Bất phương trình đúng với mọi \(3< x< 7\)
TH4: \(x>7\)
\(\left(1\right)\Leftrightarrow\left(2x-5\right)\left(x-3\right)\le x^2-6x-7\)
\(\Leftrightarrow2x^2-11x+15\le x^2-6x-7\)
\(\Leftrightarrow x^2-5x+22\le0\)
\(\Rightarrow\) vô nghiệm
Vậy ...
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