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a) \(\frac{4x + 3}{5} - \frac{6x - 2}{7}=\frac{5x + 4}{3} + 3\)
\(\Leftrightarrow \frac{21(4x +3) - 15(6x - 2)}{105}=\frac{35(5x + 4) + 315}{105}\)
<=> 21(4x + 3) - 15(6x - 2) = 35(5x + 4) + 315
<=> 84x + 63 - 90x + 30 = 175x + 140 + 315
<=> - 6x + 93 = 175x + 455
<=> - 6x - 175x = 455 - 93
<=> - 181x = 362
<=> x = - 2
Vậy ................................
b) \(\frac{3x - 11}{11} - \frac{x}{3} = \frac{3x - 5}{7} - \frac{5x - 3}{9}\)
\(\Leftrightarrow \frac{63(3x - 11) - 231x}{693}=\frac{99(3x - 5) - 77(5x - 3)}{693}\)
<=> 63(3x - 11) - 231x = 99(3x - 5) - 77(5x - 3)
<=> 189x - 693 - 231x = 297x - 495 - 385x + 231
<=> - 42x - 693 = - 88x - 264
<=> - 42x + 88x = -264 + 693
<=> 46x = 429
<=> x = \(\frac{429}{46}\)
Vậy ........
\(a,\dfrac{3\left(5x-2\right)}{4}-2=\dfrac{7x}{3}-5\left(x-7\right)\)
\(\Leftrightarrow\dfrac{15x-6-8}{4}=\dfrac{7x-15\left(x-7\right)}{3}\)
\(\Leftrightarrow\dfrac{15x-14}{4}=\dfrac{7x-15x+105}{3}\)
\(\Leftrightarrow\dfrac{45x-42}{12}=\dfrac{-32x+420}{12}\)
\(\Leftrightarrow45x+32x=420+42\)
\(\Leftrightarrow77x=462\)
\(\Leftrightarrow x=6\)
\(b,\dfrac{x+5}{2}+\dfrac{3-2x}{4}=x-\dfrac{7+x}{6}\)
\(\Leftrightarrow\dfrac{2x+10+3-2x}{4}=\dfrac{6x-7-x}{6}\)
\(\Leftrightarrow\dfrac{13}{4}=\dfrac{5x-7}{6}\)
\(\Leftrightarrow2\left(5x-7\right)=3.13\)
\(\Leftrightarrow10x-14=39\)
\(\Leftrightarrow10x=53\)
\(\Leftrightarrow x=5,3\)
\(c,\dfrac{x-3}{11}+\dfrac{x+1}{3}=\dfrac{x+7}{9}-1\)
\(\Leftrightarrow\dfrac{3x-9+11x+11}{33}=\dfrac{x+7-9}{9}\)
\(\Leftrightarrow\dfrac{14x+2}{33}=\dfrac{x-2}{9}\)
\(\Leftrightarrow33\left(x-2\right)=9\left(14x+2\right)\)
\(\Leftrightarrow33x-66=126x+18\)
\(\Leftrightarrow-93x=84\)
\(\Leftrightarrow x=-\dfrac{28}{31}\)
\(d,\dfrac{3x-0,4}{2}+\dfrac{1,5-2x}{3}=\dfrac{x+0,5}{5}\)
\(\Leftrightarrow\dfrac{3\left(3x-0,4\right)+2\left(1,5-2x\right)}{6}=\dfrac{x+0,5}{5}\)
\(\Leftrightarrow\dfrac{9x-1,2+3-4x}{6}=\dfrac{x+0,5}{5}\)
\(\Leftrightarrow\dfrac{5x+1,8}{6}=\dfrac{x+0,5}{5}\)
\(\Leftrightarrow5\left(5x+1,8\right)=6\left(x+0,5\right)\)
\(\Leftrightarrow25x+9=6x+3\)
\(\Leftrightarrow19x=-6\)
\(\Leftrightarrow x=-\dfrac{6}{19}\)
\(\Leftrightarrow77x=378\)
\(\Leftrightarrow x=\dfrac{54}{11}\)
a: \(\Leftrightarrow20x^2-12x+15x+5< 10x\left(2x+1\right)-30\)
\(\Leftrightarrow20x^2+3x+5< 20x^2+10x-30\)
=>3x+5<10x-30
=>-7x<-35
hay x>5
b: \(\Leftrightarrow4\left(5x-20\right)-6\left(2x^2+x\right)>4x\left(1-3x\right)-15x\)
\(\Leftrightarrow20x-80-12x^2-6x>4x-12x^2-15x\)
=>14x-80>-11x
=>25x>80
hay x>16/5
Mấy này bạn quy đồng lên cùng mẫu xong khử mẫu rồi giải. Dễ mà.
a: \(\Leftrightarrow7\left(7-3x\right)+12\left(5x+2\right)=84\left(x+13\right)\)
\(\Leftrightarrow49-21x+60x+24=84x+1092\)
\(\Leftrightarrow39x-84x=1092-73\)
=>-45x=1019
hay x=-1019/45
b: \(\Leftrightarrow21\left(x+3\right)-14=4\left(5x+9\right)-7\left(7x-9\right)\)
=>21x+63-14=20x+36-49x+63
=>21x+49=-29x+99
=>50x=50
hay x=1
c: \(\Leftrightarrow7\left(2x+1\right)-3\left(5x+2\right)=21x+63\)
=>14x+7-15x-6-21x-63=0
=>-22x-64=0
hay x=-32/11
d: \(\Leftrightarrow35\left(2x-3\right)-15\left(2x+3\right)=21\left(4x+3\right)-17\cdot105\)
=>70x-105-30x-45=84x+63-1785
=>40x-150-84x+1722=0
=>-44x+1572=0
hay x=393/11
a/\(\dfrac{8}{x-8}+1+\dfrac{11}{x-11}+1=\dfrac{9}{x-9}+1+\dfrac{10}{x-10}+1\)
=>\(\dfrac{8+x-8}{x-8}+\dfrac{11+x-11}{x-11}=\dfrac{9+x-9}{x-9}+\dfrac{10+x-10}{x-10}\)
=>\(\dfrac{x}{x-8}+\dfrac{x}{x-11}-\dfrac{x}{x-9}-\dfrac{x}{x-10}=0\)
=>x.\(\left(\dfrac{1}{x-8}+\dfrac{1}{x-11}+\dfrac{1}{x-9}+\dfrac{1}{x-10}\right)=0\)
=>x=0
b/\(\dfrac{x}{x-3}-1+\dfrac{x}{x-5}-1=\dfrac{x}{x-4}-1+\dfrac{x}{x-6}-1\)
=>\(\dfrac{x-x+3}{x-3}+\dfrac{x-x+5}{x-5}-\dfrac{x-x+4}{x-4}-\dfrac{x-6+6}{x-6}=0\)
=>\(\dfrac{3}{x-3}+\dfrac{5}{x-5}-\dfrac{4}{x-4}-\dfrac{6}{x-6}=0\)
Đến đây thì bạn giải giống câu a
\(\dfrac{3x-11}{11}-\dfrac{x}{3}=\dfrac{3x-5}{7}-\dfrac{5x-3}{9}\)
\(\Rightarrow\dfrac{3\left(3x-11\right)}{33}-\dfrac{11x}{33}=\dfrac{9\left(3x-5\right)}{63}-\dfrac{7\left(5x-3\right)}{63}\)
\(\Rightarrow\dfrac{3\left(3x-11\right)-11x}{33}=\dfrac{9\left(3x-5\right)-7\left(5x-3\right)}{63}\)
\(\Rightarrow\dfrac{9x-33-11x}{33}=\dfrac{27x-45-35x+21}{63}\)
\(\Rightarrow\dfrac{-2x-33}{33}=\dfrac{-8x-24}{63}\)
\(\Rightarrow63\left(-2x-33\right)=33\left(-8x-24\right)\)
\(\Rightarrow-126x-2079=-264x-792\)
\(\Rightarrow-126x+264x=-792+2079\)
\(\Rightarrow138x=1287\)
\(\Rightarrow x=\dfrac{1287}{138}\)
\(\Rightarrow x=\dfrac{429}{46}\)