Tìm a/b biết
A. a/b : 2/3 = 3/5 - 1/10
B. a/b * 1/5 = 3/5 + 1
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a: \(\dfrac{4}{5}-\dfrac{5}{6}< =\dfrac{x}{30}< =\dfrac{1}{3}-\dfrac{3}{10}\)
=>\(\dfrac{24-25}{30}< =\dfrac{x}{30}< =\dfrac{10-9}{30}\)
=>\(\dfrac{-1}{30}< =\dfrac{x}{30}< =\dfrac{1}{30}\)
=>-1<=x<=1
mà x nguyên
nên \(x\in\left\{-1;0;1\right\}\)
b: \(\dfrac{a}{7}+\dfrac{1}{14}=\dfrac{-1}{b}\)
=>\(\dfrac{2a+1}{14}=\dfrac{-1}{b}\)
=>\(\left(2a+1\right)\cdot b=-14\)
mà 2a+1 lẻ (do a là số nguyên)
nên \(\left(2a+1\right)\cdot b=1\cdot\left(-14\right)=\left(-1\right)\cdot14=7\cdot\left(-2\right)=\left(-7\right)\cdot2\)
=>\(\left(2a+1;b\right)\in\left\{\left(1;-14\right);\left(-1;14\right);\left(7;-2\right);\left(-7;2\right)\right\}\)
=>\(\left(a;b\right)\in\left\{\left(0;-14\right);\left(-1;14\right);\left(3;-2\right);\left(-4;2\right)\right\}\)
bạn đăg tách ra cho m.n cùng giúp nhé
Bài 2 :
a, \(A=\left|2x-4\right|+2\ge2\)
Dấu ''='' xảy ra khi x = 2
Vậy GTNN A là 2 khi x = 2
b, \(B=\left|x+2\right|-3\ge-3\)
Dấu ''='' xảy ra khi x = -2
Vậy GTNN B là -3 khi x = -2
b) \(9x-2:3^2=3^4\)
\(9x-2:9=81\)
\(2:9=9x-81\)
\(\dfrac{2}{9}=9x-81\)
\(9x=81+\dfrac{2}{9}\)
\(9x=\dfrac{731}{9}\)
\(x=\dfrac{731}{9}:9\)
\(x=\dfrac{731}{81}\)
\(a.5x-5^2=10\) \(b.9x-2:3^2=3^4\)
\(5x=10+5^2\) \(9x-2=3^4.3^2\)
\(5x=35\) \(9x-2=729\)
\(x=35:5=7\) \(9x=729+2=731\)
\(x=731:9\)
\(x=\dfrac{731}{81}\)
\(c=10x+\left(2^2\right).5=10^2\)
\(10x+20=100\)
\(10x=100-20\)
\(10x=80\)
\(x=80:10=8\)
a)Vì a<b=>2a<2b
=>2a+5<2b+5
b)Vì a<b=>-10a>-10b
=>2-10a>2-10b
c)Vì a<b=>7a<7b
=>7a-3<7b-3(1)
Vì -3<-1=>7b-3<7b-1(2)
Từ (1) và (2)=>đpcm
d)Vì a<b=>\(-\dfrac{a}{3}< -\dfrac{b}{3}\)
=>\(3-\dfrac{a}{3}>3-\dfrac{b}{3}\)(3)
Vì 3>1=>\(3-\dfrac{b}{3}>1-\dfrac{b}{3}\)(4)
Từ (3) và (4)=> đpcm
a, Ta có: a < b \(\Rightarrow\) 2a < 2b \(\Rightarrow\) 2a + 5 < 2b + 5
b, Ta có: a < b \(\Rightarrow\) -10a > -10b (đổi dấu) \(\Rightarrow\) 2 + (-10a) > 2 + (-10b) \(\Leftrightarrow2-10a>2-10b\)
c, Ta có: a < b \(\Rightarrow\)7a < 7b
Lại có: -3 < -1
\(\Rightarrow\) 7a + (-3) < 7a + (-1) \(\Leftrightarrow\) 7a - 3 < 7b - 1
d, Ta có: a < b \(\Rightarrow-\dfrac{a}{3}>-\dfrac{b}{3}\)(đổi dấu)
Lại có: 3 > 1
\(\Rightarrow3+\left(-\dfrac{a}{3}\right)>1+\left(-\dfrac{b}{3}\right)\Leftrightarrow3-\dfrac{a}{3}>1-\dfrac{b}{3}\)
a: =>1/3(2x-5)=-2/3-3/2=-4/6-9/6=-13/6
=>2x-5=-13/6*3=-13/2
=>2x=-3/2
=>x=-3/4
b: =>2/5x=-3/4-1/2=-5/4
=>x=-5/4:2/5=-5/4*5/2=-25/8
a)
\(-\dfrac{2}{3}-\dfrac{1}{3}\left(2x-5\right)=\dfrac{3}{2}\\ \Rightarrow\dfrac{1}{3}\left(2x-5\right)=-\dfrac{2}{3}-\dfrac{3}{2}\\ \Rightarrow\dfrac{1}{3}\left(2x-5\right)=-\dfrac{13}{6}\\ \Rightarrow2x-5=-\dfrac{13}{6}:\dfrac{1}{3}=-\dfrac{13}{2}\\ \Rightarrow2x=-\dfrac{13}{2}+5\\ \Rightarrow2x=-\dfrac{3}{2}\\ \Rightarrow x=-\dfrac{3}{2}:2\\ \Rightarrow x=-\dfrac{3}{4}\)
b)
\(\dfrac{2}{5}x+\dfrac{1}{2}=-\dfrac{3}{4}\\ \Rightarrow\dfrac{2}{5}x=-\dfrac{3}{4}-\dfrac{1}{2}\\ \Rightarrow\dfrac{2}{5}x=-\dfrac{5}{4}\\ \Rightarrow x=-\dfrac{5}{4}:\dfrac{2}{5}=-\dfrac{25}{8}\)
\(\frac{a}{3}=\frac{4b}{5}\Rightarrow\frac{a}{3.\frac{3}{10}}=\frac{b}{\frac{5}{4}.\frac{3}{10}}\Rightarrow\frac{a}{\frac{9}{10}}=\frac{b}{\frac{3}{8}}\)
\(\frac{10b}{3}=\frac{5c}{2}\Rightarrow\frac{b}{\frac{3}{10}.\frac{5}{4}}=\frac{c}{\frac{2}{5}.\frac{5}{4}}\Rightarrow\frac{b}{\frac{3}{8}}=\frac{c}{\frac{1}{2}}\)
=> \(\frac{a}{\frac{9}{10}}=\frac{b}{\frac{3}{8}}=\frac{c}{\frac{1}{2}}\)
Áp dụng dãy tỉ số bằng nhau: \(\frac{a}{\frac{9}{10}}=\frac{b}{\frac{3}{8}}=\frac{c}{\frac{1}{2}}=\frac{a+b+c}{\frac{9}{10}+\frac{3}{8}+\frac{1}{2}}=\frac{142}{\frac{71}{40}}=80\)
=> a = 80.9/10=72
b = 80.3/8 =30
c = 80. 1/2 =40
Lời giải:
a.
$0< x< \frac{1}{4}+\frac{4}{5}$
$\Rightarrow 0< x< \frac{21}{20}$ hay $0< x< 1,05$
$\Rightarrow x=1$
b.
$\frac{4}{7}+\frac{3}{7}< x< \frac{5}{3}+\frac{2}{3}$
$\Rightarrow 1< x< \frac{7}{3}$
$\Rightarrow x=2$
a) \(\frac{a}{b}:\frac{2}{3}=\frac{3}{5}-\frac{1}{10}\)
\(\Rightarrow\frac{a}{b}:\frac{2}{3}=\frac{6}{10}-\frac{1}{10}\)
\(\Rightarrow\frac{a}{b}:\frac{2}{3}=\frac{5}{10}\)
\(\Rightarrow\frac{a}{b}=\frac{5}{10}x\frac{2}{3}\)
\(\Rightarrow\frac{a}{b}=\frac{10}{30}\)
\(\Rightarrow\frac{a}{b}=\frac{1}{3}\)
b, \(\frac{a}{b}x\frac{1}{5}=\frac{3}{5}+1\)
\(\Rightarrow\frac{a}{b}x\frac{1}{5}=\frac{3}{5}+\frac{5}{5}\)
\(\Rightarrow\frac{a}{b}x\frac{1}{5}=\frac{8}{5}\)
\(\Rightarrow\frac{a}{b}=\frac{8}{5}:\frac{1}{5}\)
\(\Rightarrow\frac{a}{b}=\frac{8}{5}x5\)
\(\Rightarrow\frac{a}{b}=8\)