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1)
\(\frac{7.8^3-5.2^{10}}{\left(-16\right)^2}\)
= \(\frac{7.2^8.2-5.2^8.2^2}{16^2}\)
= \(\frac{2^8.\left(2.7-5.2^2\right)}{2^8}\)
= \(\frac{2^8.\left(-6\right)}{2^8}\)
= \(-6\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\Leftrightarrow\frac{-2}{17}\le\frac{x}{17}\le\frac{2}{17}\Rightarrow x\in\left(-2;-1;0;1;2\right)\)
\(\Leftrightarrow\frac{-1}{24}\le\frac{x}{24}\le\frac{5}{24}\Rightarrow x\in\left(-1;0;1;2;3;4;5\right)\)
2 câu sau tự làm nha
\(-\frac{5}{17}+\frac{3}{17}\le\frac{x}{17}\le\frac{13}{17}+-\frac{11}{17}\)
\(\frac{-2}{17}\le\frac{x}{17}\le\frac{2}{17}\)
=> \(x\in\left\{-2;-1;0;1;2\right\}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(-5\le x\le5\)
\(\Rightarrow x=\left\{-5;-4;-3;....;3;4;5\right\}\)
Tổng của các số nguyên x là:
\(\left(-5+5\right)+\left(-4+4\right)+\left(-3+3\right)+\left(-2+2\right)+\left(-1+1\right)+0=0\)
b) \(-7\le x< 10\Rightarrow x=\left\{-7;-6;-5;....;8;9\right\}\)
Tổng các số nguyên x là: (-7+7)+(-6+6)+....+(-1+1)+0+8+9 = 17
Câu c và d: Tương tự
c) Tổng các số nguyên x là: (-12+12)+(-11+11)+...+(-1+1)+0+(-14)+(-13) = -27
d) Tổng các số nguyên x là: (-100+100)+(-99+99)+....+(-1+1)+0 = 0
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a)\frac{1}{3}+\frac{-2}{5}+\frac{1}{6}+\frac{-1}{5}\le x< \frac{-3}{4}+\frac{2}{7}+\frac{-1}{4}+\frac{3}{5}+\frac{5}{7}\)
\(\Rightarrow\frac{1}{3}+\frac{1}{6}+\frac{-2}{5}+\frac{-1}{5}\le x< \frac{-3}{4}+\frac{-1}{4}+\frac{2}{7}+\frac{5}{7}+\frac{3}{5}\)
\(\Rightarrow\frac{2}{6}+\frac{1}{6}+\frac{-3}{5}\le x< -1+1+\frac{3}{5}\)
\(\Rightarrow\frac{1}{2}+\frac{-3}{5}\le x< \frac{3}{5}\)
\(\Rightarrow\frac{-1}{10}\le x< \frac{6}{10}\)
\(\Rightarrow-1\le x< 6\)
\(\Rightarrow x\in\left\{-1;0;1;2;3;4;5\right\}\)
Bài b tương tự
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(\frac{2}{3}\left(\frac{1}{2}+\frac{3}{4}-\frac{1}{3}\right)\le\frac{x}{18}\)
\(\frac{x}{18}\le\frac{7}{3}\left(\frac{1}{2}-\frac{1}{6}\right)\)
tu tim x o 2 truong hop tren
b) de \(\frac{11}{2x+1}\) nguyen thi \(2x+1\inƯ\left(11\right)=\left\{\pm1;\pm11\right\}\)
2x+1=-1 suy ra x=-1
2x+1=1 suy ra x=0
2x+1=11 suy ra x=5
2x+1=-11 suy ra x=-6
Vay de ......thi x thuoc {-1;0;5;6}
=> \(-\frac{70}{7}\le\frac{7x}{7}\le-\frac{11}{7}\)
=> \(-70\le7x\le-11\)
=> 7x \(\in\) {-70; -69; -68; ...;-11}
Để x nguyên thì 7x \(\in\) B(7)
=> 7x \(\in\) {-70; -63; -56; -49;-42;-35;-28;-21;-14}
=> x \(\in\) {-10; -9; -8; -7; -6;-5;-4; -3;-2}