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Bài 3
\(\frac{x-1}{9}=\frac{8}{3}\)
\(\Rightarrow\left(x-1\right).3=8.9\)
\(\Rightarrow\left(x-1\right).3=72\)
\(\Rightarrow x-1=24\)
\(\Rightarrow x=25\)
\(\frac{-x}{4}=\frac{-9}{x}\)
\(\Rightarrow\left(-x\right).x=\left(-9\right).4\)
\(\Rightarrow-x=-36\)
\(\Rightarrow x=36\)
\(\frac{x}{4}=\frac{18}{x+1}\)
\(\Rightarrow x.\left(x+1\right)=4.18\)
\(\Rightarrow x.\left(x+1\right)=72\)
Vì x và x + 1 là 2 số tự nhiên liên tiếp
\(\Rightarrow x\left(x+1\right)=8.9\)
\(\Rightarrow\orbr{\begin{cases}x=8\\x=8\end{cases}}\)
Bài 4
\(\frac{x-4}{y-3}=\frac{4}{3},x-y=5\)
Ta có :
\(x-y=5\)
\(\Rightarrow x=5+y\)
\(\Rightarrow\frac{y+5-4}{y-3}=\frac{4}{3}\)
\(\Rightarrow\frac{y+1}{y-3}=\frac{4}{3}\)\(\)
\(\Rightarrow\left(y+1\right).3=\left(y-3\right).4\)
\(\Rightarrow y.3+1.3=y.4-3.4\)
\(\Rightarrow y.3+3=y.4-12\)
\(\Rightarrow y.3-y.4=-12-3\)
\(\Rightarrow-1y=-15\)
\(\Rightarrow y=\left(-15\right):\left(-1\right)\)
\(\Rightarrow y=15\)
Vì x = y + 5
\(\Rightarrow x=15+4\)
\(\Rightarrow x=19\)
Vậy x = 19 , y = 15
\(\frac{-x}{4}=\frac{-9}{x}\)
\(\Rightarrow\left(-x\right).x=4.\left(-9\right)\)
\(\Rightarrow-x=-9;x=4\)
\(\Rightarrow x=9;x=4\)
\(\frac{x}{7}=\frac{x+1}{14}\Leftrightarrow14x=7x+7\Leftrightarrow7x=7\Leftrightarrow x=1\)
\(\frac{1}{2}+\frac{1}{3}+\frac{1}{6}\le x\le\frac{15}{4}+\frac{18}{8}\)
\(\Leftrightarrow1\le x\le6\Leftrightarrow x=1;2;3;4;5;6\)
\(\frac{1}{2}+\frac{-3}{5}+\frac{1}{10}\le x\le\frac{8}{3}+\frac{14}{6}\)
\(\Leftrightarrow\frac{1}{2}-\frac{3}{5}+\frac{1}{10}\le x\le\frac{8}{3}+\frac{14}{6}\)
\(\Leftrightarrow0\le x\le5\Leftrightarrow x=0;1;2;3;4;5\)
\(\frac{x}{7}=\frac{x+1}{14}\)
=> \(\frac{x\cdot2}{7\cdot2}=\frac{x+1}{14}\)
=> \(2x=x+1\)
=> \(2x-x-1=0\)
=> \(1x-1=0\)
=> \(x=1\)
\(\frac{1}{2}+\frac{1}{3}+\frac{1}{6}\le x\le\frac{15}{4}+\frac{18}{8}\)
=> \(1\le x\le6\)
=> \(x=\left\{1;2;3;4;5;6\right\}\)
\(\frac{1}{2}+\frac{-3}{5}+\frac{1}{10}\le x\le\frac{8}{3}+\frac{14}{6}\)
=> \(0\le x\le5\)
=> \(x=\left\{0;1;2;3;4;5\right\}\)
Bài 1: Tìm x biết:
1) x +\(\frac{7}{12}\)= \(\frac{17}{18}\)- \(\frac{1}{9}\) 2) \(\frac{29}{30}\)- (\(\frac{13}{23}\)+ x) = \(\frac{7}{69}\)
x +\(\frac{7}{12}\)= \(\frac{15}{18}\) \(\frac{13}{23}\)+ x = \(\frac{29}{30}\)- \(\frac{7}{69}\)
x = \(\frac{15}{18}\)- \(\frac{7}{12}\) \(\frac{13}{23}\)+ x = \(\frac{199}{230}\)
x = \(\frac{1}{4}\) x = \(\frac{3}{10}\)
bài 1
\(\frac{6}{-a^2-1}=\frac{-6}{a^2+1}\) thế này ms đúng ^.^
bài 2
a) \(\frac{111}{37}< x< \frac{91}{13}\Leftrightarrow\frac{1443}{481}< x< \frac{3367}{481}\)
\(\Rightarrow3< x< 7\Rightarrow x\in\left\{4;5;6\right\}\)
b) \(\frac{-84}{14}< 3x< \frac{108}{9}\Leftrightarrow\frac{-756}{126}< 3x< \frac{1512}{126}\\ \Leftrightarrow-6< 3x< 12\Leftrightarrow-2< x< 4\)
vậy\(x\in\left\{-1;0;1;2;3\right\}\)
a)\(\frac{-5}{6}\).\(\frac{120}{25}\)<x<\(\frac{-7}{15}\).\(\frac{9}{14}\)
-4 <x<\(\frac{-3}{10}\)
\(\frac{-40}{10}\)< x <\(\frac{-3}{10}\)=>x E {-39:-38:-37:.....:-4}
b)\(\left(\frac{-5}{3}\right)^3\)<x<\(\frac{-24}{35}.\frac{-5}{6}\)
\(\frac{-875}{189}< x< \frac{108}{189}\)
=> x E {\(\frac{-874}{189},\frac{-873}{189},......,\frac{107}{189}\)}
\(\frac{1}{2}+\frac{1}{3}+\frac{1}{6}=\frac{3}{6}+\frac{2}{6}+\frac{1}{6}=\frac{6}{6}=1\)
\(\frac{13}{14}+\frac{14}{8}=\frac{13.4}{14.4}+\frac{14.7}{8.7}=\frac{52}{56}+\frac{98}{56}=\frac{150}{56}\simeq2,68\)
Như vậy: \(1\le x\le2,68\)
Mà x thuộc N => x=1 và x=2
Đáp số: x=1 và x=2