a) \(\dfrac{-11}{15}< \dfrac{x}{15}< \dfrac{-8}{15}\)
b) \(\dfrac{3}{7}< \dfrac{x}{21}< \dfrac{2}{3}\)
c) \(\dfrac{-67}{21}< \dfrac{x}{168}< \dfrac{-3}{8}\)
a) Ta có: \(\dfrac{-11}{15}< \dfrac{x}{15}< \dfrac{-8}{15}\)
nên -11<x<-8
hay \(x\in\left\{-10;-9\right\}\)
b) Ta có: \(\dfrac{3}{7}< \dfrac{x}{21}< \dfrac{2}{3}\)
\(\Leftrightarrow\dfrac{9}{21}< \dfrac{x}{21}< \dfrac{14}{21}\)
Suy ra: 9<x<14
hay \(x\in\left\{10;11;12;13\right\}\)
c) Ta có: \(\dfrac{-67}{21}< \dfrac{x}{168}< \dfrac{-3}{8}\)
nên \(\dfrac{-536}{168}< \dfrac{x}{168}< \dfrac{-63}{168}\)
Suy ra: -536<x<-63
hay \(x\in\left\{-535;-534;...;-64\right\}\)
Viết tập hợp A các số tự nhiên x sao cho:
a, \(\dfrac{-36}{9}\) ≤ x < \(\dfrac{-15}{5}\)
b, \(\dfrac{-27}{3}\) < x ≤ \(\dfrac{12}{4}\)
c, \(\dfrac{-21}{7}\) < x < \(\dfrac{-12}{6}\)
a: \(\Leftrightarrow-4< =x< =-3\)
hay \(x\in\varnothing\)
b: =>-9<x<=3
hay \(x\in\left\{0;1;2;3\right\}\)
Tìm x, biết:
a) \(\left(3\dfrac{1}{2}-2.x\right).3\dfrac{1}{3}=7\dfrac{1}{3}\)
b) \(\dfrac{4}{9}.x=\dfrac{9}{8}-0,125\)
c) \(\dfrac{-X}{21}=\dfrac{20}{7}\)
a, \(\left(\dfrac{7}{2}-2x\right).\dfrac{10}{3}=\dfrac{22}{3}\Leftrightarrow\dfrac{7}{2}-2x=\dfrac{22}{10}=\dfrac{11}{5}\)
\(\Leftrightarrow2x=\dfrac{13}{10}\Leftrightarrow x=\dfrac{13}{20}\)
b, \(\dfrac{4x}{9}=\dfrac{9}{8}-\dfrac{125}{1000}=1\Leftrightarrow x=\dfrac{9}{4}\)
c, \(-\dfrac{x}{21}=\dfrac{60}{21}\Rightarrow x=-60\)
tìm x :
a, x . \(\dfrac{-5}{8}\) = \(\dfrac{15}{32}\) b, \(\dfrac{3}{10}\) : x =\(\dfrac{-9}{20}\)
c, \(\dfrac{-1}{4}\) x + \(\dfrac{4}{5}\) =\(\dfrac{3}{4}\) d, \(\dfrac{-7}{8}\) + \(\dfrac{2}{3}\) :x = \(\dfrac{3}{5}\) . \(\dfrac{-5}{12}\)
\(a,x.\dfrac{-5}{8}=\dfrac{15}{32}\)
\(\Leftrightarrow x=\dfrac{15}{32}:\dfrac{-5}{8}\)
\(\Leftrightarrow x=\dfrac{15}{32}.\dfrac{-8}{5}\)
\(\Leftrightarrow x=-\dfrac{3}{4}\)
\(b,\dfrac{3}{10}:x=-\dfrac{9}{20}\)
\(\Leftrightarrow x=\dfrac{3}{10}:\dfrac{-9}{20}\)
\(\Leftrightarrow x=\dfrac{3}{10}.\dfrac{-20}{9}\)
\(\Leftrightarrow x=-\dfrac{2}{3}\)
\(c,-\dfrac{1}{4}x+\dfrac{4}{5}=\dfrac{3}{4}\)
\(\Leftrightarrow-\dfrac{1}{4}x=\dfrac{3}{4}-\dfrac{4}{5}\)
\(\Leftrightarrow-\dfrac{1}{4}x=-\dfrac{1}{20}\)
\(\Leftrightarrow x=-\dfrac{1}{20}\times\left(-4\right)\)
\(\Leftrightarrow x=\dfrac{1}{5}\)
\(d,-\dfrac{7}{8}+\dfrac{2}{3}:x=\dfrac{3}{5}.\dfrac{-5}{12}\)
\(\Leftrightarrow-\dfrac{7}{8}+\dfrac{2}{3}:x=-\dfrac{1}{4}\)
\(\Leftrightarrow\dfrac{2}{3}:x=-\dfrac{1}{4}+\dfrac{7}{8}\)
\(\Leftrightarrow\dfrac{2}{3}:x=\dfrac{5}{8}\)
\(\Leftrightarrow x=\dfrac{2}{3}:\dfrac{5}{8}\)
\(\Leftrightarrow x=\dfrac{16}{15}\)
a, \(x\cdot\dfrac{-5}{8}=\dfrac{15}{32}\)
\(x=\dfrac{15}{32}:\dfrac{-5}{8}\)
\(x=\dfrac{-3}{4}\)
b, \(\dfrac{3}{10}:x=\dfrac{-9}{20}\)
\(x=\dfrac{3}{10}:\dfrac{-9}{20}\)
\(x=-\dfrac{2}{3}\)
c, \(\dfrac{-1}{4}x+\dfrac{4}{5}=\dfrac{3}{4}\)
\(\dfrac{-1}{4}x=\dfrac{3}{4}-\dfrac{4}{5}\)
\(\dfrac{-1}{4}x=-\dfrac{1}{20}\)
\(x=-\dfrac{1}{20}:\dfrac{-1}{4}\)
\(x=\dfrac{1}{5}\)
d, \(\dfrac{-7}{8}+\dfrac{2}{3}:x=\dfrac{3}{5}\cdot\dfrac{-5}{12}\)
\(\dfrac{-7}{8}+\dfrac{2}{3}:x=-\dfrac{1}{4}\)
\(\dfrac{2}{3}:x=-\dfrac{1}{4}+\dfrac{-7}{8}\)
\(\dfrac{2}{3}:x=\dfrac{5}{8}\)
\(x=\dfrac{2}{3}:\dfrac{5}{8}\)
\(x=\dfrac{16}{15}\)
#YVA6
\(a,x.\dfrac{-5}{8}=\dfrac{15}{32} \)
\(x=\dfrac{15}{32}:\dfrac{-5}{8}\)
\(x=\dfrac{-3}{4}\)
\(b,\dfrac{3}{10}:x=\dfrac{-9}{20}\)
\(x=\dfrac{3}{10}:\dfrac{-9}{20}\)
\(x=\dfrac{-2}{3}\)
\(c,\dfrac{-1}{4}.x+\dfrac{4}{5}=\dfrac{3}{4}\)
\(\dfrac{-1}{4}.x=\dfrac{-1}{20}\)
\(x=\dfrac{-1}{20}:\dfrac{-1}{4}\)
\(x=\dfrac{1}{5}\)
\(d,\dfrac{-7}{8}+\dfrac{2}{3}:x=\dfrac{3}{5}.\dfrac{-5}{12}\)
\(\dfrac{-7}{8}+\dfrac{2}{3}:x=\dfrac{-1}{4}\)
\(\dfrac{2}{3}:x=\dfrac{5}{8}\)
\(x=\dfrac{16}{15}\)
\(#yH\)
\(#NBaoNgoc\)
Bài 15:
a)\(\dfrac{-2}{5}\)+\(\dfrac{4}{5}\) . x =\(\dfrac{3}{5}\)
b)\(\dfrac{-3}{7}\) - \(\dfrac{4}{7}\):x = -2
Bài 16
a) x - \(\dfrac{10}{3}\) = \(\dfrac{7}{15}\) . \(\dfrac{3}{5}\)
b) x + \(\dfrac{3}{22}\)= \(\dfrac{27}{121}\) . \(\dfrac{11}{9}\)
c) \(\dfrac{8}{23}\) . \(\dfrac{48}{24}\) - x = \(\dfrac{1}{3}\)
d) 1 - x = \(\dfrac{49}{65}\).\(\dfrac{5}{7}\)
Bài 17: tìm x
a) \(\dfrac{62}{7}\) . x = \(\dfrac{29}{9}\): \(\dfrac{3}{56}\)
b) \(\dfrac{1}{5}\) : x=\(\dfrac{1}{5}\)+\(\dfrac{1}{7}\)
bài 18:
a)\(\dfrac{2}{5}\)+\(\dfrac{3}{4}\): x =\(\dfrac{-1}{2}\)
b)\(\dfrac{5}{7}\) - \(\dfrac{2}{3}\) . x = \(\dfrac{4}{5}\)
c) \(\dfrac{1}{2}\)x + \(\dfrac{3}{5}\)x = \(\dfrac{-2}{3}\)
d) \(\dfrac{4}{7}\).x-x = \(\dfrac{-9}{14}\)
bài 19: tính
\(\dfrac{1}{1.2}\)+\(\dfrac{1}{2.3}\)+\(\dfrac{1}{3.4}\)+...+ \(\dfrac{1}{2018.2019}\)
bài 20:tìm x
\(\dfrac{1}{1.2}\)+\(\dfrac{1}{2.3}\)+...+\(\dfrac{1}{x.\left(x+1\right)}\)=\(\dfrac{2008}{2009}\)
bài 21: tìm x
\(\dfrac{x+1}{99}\)+\(\dfrac{x+2}{98}\)\(\dfrac{x+3}{97}\)\(\dfrac{x+4}{96}\)=-4
bài 22 : so sánh các phân số sau:
a) \(\dfrac{-1}{5}\)+\(\dfrac{4}{-5}\)và 1
b) \(\dfrac{3}{5}\) và \(\dfrac{2}{3}\)+\(\dfrac{-1}{5}\)
c)\(\dfrac{3}{2}\)+\(\dfrac{-4}{3}\) và \(\dfrac{1}{10}\)+\(\dfrac{-4}{5}\)
d) \(\dfrac{1}{2}\)+\(\dfrac{1}{3}\)+\(\dfrac{1}{4}\)+\(\dfrac{1}{5}\)+\(\dfrac{1}{6}\) và 2
\(\dfrac{16}{21}\) + \(\dfrac{6}{7}\) ; \(\dfrac{15}{22}\) x \(\dfrac{11}{35}\) ; \(\dfrac{8}{11}\) : \(\dfrac{5}{22}\) ; \(\dfrac{9}{13}\) : \(\dfrac{27}{39}\) .
`# \text {DNamNgV}`
`16/21 + 6/7`
`= 16/21 + 18/21`
`= 34/21`
__
`15/22 \times 11/35`
`= (15 \times 11)/(22 \times 35)`
`= (5 \times 3 \times 11)/(2 \times 11 \times 5 \times 7)`
`= (3 \times 1)/(2 \times 7)`
`= 3/14`
___
`8/11 \div 5/22`
`= 8/11 \times 22/5`
`= (8 \times 22)/(11 \times 5)`
`= (8 \times 11 \times 2)/(11 \times 5)`
`= (8 \times 2)/5`
`= 16/5`
___
`9/13 \div 27/39`
`= 9/13 \times 39/27`
`= 9/13 \times 13/9`
`= 1`
\(a,\dfrac{15-x}{14}=\dfrac{5}{7}\)
\(b,\dfrac{x}{9}=\dfrac{17}{3}\)
\(c,15-\dfrac{x}{2}=\dfrac{3}{7}\)
Tìm x
\(\dfrac{15-x}{14}=\dfrac{5}{7}\\ \left(15-x\right)\times7=5\times14\\ \left(15-x\right)\times7=70\\ 15-x=70:7\\ 15-x=10\\ x=15-10\\ x=5\)
__
\(\dfrac{x}{9}=\dfrac{17}{3}\\ x\times3=17\times9\\ x\times3=153\\ x=153:3\\ x=51\)
__
\(15-\dfrac{x}{2}=\dfrac{3}{7}\\ \dfrac{x}{2}=15-\dfrac{3}{7}\\ \dfrac{x}{2}=\dfrac{102}{7}\\ x\times7=102\times2\\ x\times7=204\\ x=204:7\\ x=\dfrac{204}{7}\)
1/ Tìm x,y biết:
a/ \(\dfrac{x}{2}\) = \(\dfrac{y}{5}\) và x+y=-21
b/ 7x = 3y và x-y=16
c/ \(\dfrac{x}{y}\) = \(\dfrac{5}{9}\) và 3x+2x=66
d/ \(\dfrac{x}{15}\) = \(\dfrac{y}{7}\) và x-2y=16
e/ \(\dfrac{x}{5}\) = \(\dfrac{y}{2}\) và x × y = 1000
2/ Tìm x,y,z biết
\(\dfrac{x}{13}\) = \(\dfrac{y}{7}\) = \(\dfrac{z}{5}\) và x-y-z=6
a. Áp dụng tính chất dãy tỉ số bằng nhau:
$\frac{x}{2}=\frac{y}{5}=\frac{x+y}{2+5}=\frac{-21}{7}=-3$
$\Rightarrow x=2(-3)=-6; y=5(-3)=-15$
b. Áp dụng tính chất dãy tỉ số bằng nhau:
$7x=3y=\frac{x}{\frac{1}{7}}=\frac{y}{\frac{1}{3}}=\frac{x-y}{\frac{1}{7}-\frac{1}{3}}=\frac{16}{\frac{-4}{21}}=-84$
$\Rightarrow x=(-84):7=-12; y=-84:3=-28$
c. $\frac{x}{y}=\frac{5}{9}\Rightarrow \frac{x}{5}=\frac{y}{9}$
Áp dụng tính chất dãy tỉ số bằng nhau:
$\frac{x}{5}=\frac{y}{9}=\frac{3x}{15}=\frac{2y}{18}=\frac{3x+2y}{15+18}=\frac{66}{33}=2$
$\Rightarrow x=2.5=10; y=9.2=18$
d. Áp dụng tính chất dãy tỉ số bằng nhau:
$\frac{x}{15}=\frac{y}{7}=\frac{2y}{14}=\frac{x-2y}{15-14}=\frac{16}{1}=16$
$\Rightarrow x=16.15=240; y=7.16=112$
e.
Đặt $\frac{x}{5}=\frac{y}{2}=k\Rightarrow x=5k ; y=2k$
Khi đó: $xy=5k.2k=10k^2=1000\Rightarrow k^2=100\Rightarrow k=\pm 10$
Với $k=10$ thì $x=5k=50; y=2k=20$
Với $k=-10$ thì $x=5k=-50; y=2k=-20$
Bài 2:
Áp dụng tính chất dãy tỉ số bằng nhau:
$\frac{x}{13}-\frac{y}{7}-\frac{z}{5}=\frac{x-y-z}{13-7-5}=\frac{6}{1}=6$
$\Rightarrow x=13.6=78; y=7.6=42; z=5.6=30$
Bài 1:
a,\(|x-3|+|2-x|=0\)
b,\(\left(2-\dfrac{3}{4}x\right).\left(x+1\right)=0\)
bài 2:
a,A=\(\dfrac{\dfrac{-6}{7}+\dfrac{6}{13}-\dfrac{6}{29}}{\dfrac{9}{7}-\dfrac{9}{13}+\dfrac{9}{29}}\)
b,B=\(\dfrac{\dfrac{2}{15}-\dfrac{2}{21}+\dfrac{2}{39}}{0,25-\dfrac{5}{28}+\dfrac{5}{52}}\)
c,C=\(\dfrac{50-\dfrac{4}{15}+\dfrac{2}{15}-\dfrac{2}{17}}{100-\dfrac{8}{13}+\dfrac{4}{15}-\dfrac{4}{17}}:\dfrac{1+\dfrac{2}{21}-\dfrac{5}{121}}{\dfrac{65}{121}-\dfrac{26}{71}-13}\)
1.a) Dễ nhận thấy đề toán chỉ giải được khi đề là tìm x,y. Còn nếu là tìm x ta nhận thấy ngay vô nghiệm. Do đó: Sửa đề: \(\left|x-3\right|+\left|2-y\right|=0\)
\(\Leftrightarrow\left|x-3\right|=\left|2-y\right|=0\)
\(\left|x-3\right|=0\Rightarrow\left\{{}\begin{matrix}x-3=0\\-\left(x-3\right)=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\x=-3\end{matrix}\right.\) (1)
\(\left|2-y\right|=0\Rightarrow\left\{{}\begin{matrix}2-y=0\\-\left(2-y\right)=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=2\\y=-2\end{matrix}\right.\) (2)
Từ (1) và (2) có: \(\left[{}\begin{matrix}\left\{{}\begin{matrix}x_1=3\\x_2=-3\end{matrix}\right.\\\left\{{}\begin{matrix}y_1=2\\y_2=-2\end{matrix}\right.\end{matrix}\right.\)
Bài 2:
a: \(=\dfrac{-6\left(\dfrac{1}{7}-\dfrac{1}{13}+\dfrac{1}{29}\right)}{9\left(\dfrac{1}{7}-\dfrac{1}{13}+\dfrac{1}{29}\right)}=\dfrac{-6}{9}=\dfrac{-2}{3}\)
b: \(=\dfrac{\dfrac{2}{15}-\dfrac{2}{21}+\dfrac{2}{39}}{\dfrac{10}{40}-\dfrac{10}{56}+\dfrac{10}{104}}\)
\(=\dfrac{\dfrac{2}{3}\left(\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{13}\right)}{\dfrac{10}{8}\left(\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{13}\right)}=\dfrac{2}{3}:\dfrac{5}{4}=\dfrac{2}{3}\cdot\dfrac{4}{5}=\dfrac{8}{15}\)
c: \(=\dfrac{2\left(25-\dfrac{2}{13}+\dfrac{1}{15}-\dfrac{1}{17}\right)}{4\left(25-\dfrac{2}{13}+\dfrac{1}{15}-\dfrac{1}{17}\right)}:\dfrac{1+\dfrac{2}{21}-\dfrac{5}{121}}{13\left(\dfrac{5}{121}-\dfrac{2}{21}-1\right)}\)
=2/4:(-1)/13=2/4x(-13)=-13/2
