Câu 3: Giải các phương trình sau bằng cách đưa về dạng ax+b=0
1. a, \(\frac{5x-2}{3}=\frac{5-3x}{2}\); b, \(\frac{10x+3}{12}=1+\frac{6+8x}{9}\)
c, \(2\left(x+\frac{3}{5}\right)=5-\left(\frac{13}{5}+x\right)\); d, \(\frac{7}{8}x-5\left(x-9\right)=\frac{20x+1,5}{6}\)
e, \(\frac{7x-1}{6}+2x=\frac{16-x}{5}\); f, 4 (0,5-1,5x)=\(\frac{5x-6}{3}\)
g, \(\frac{3x+2}{2}-\frac{3x+1}{6}=\frac{5}{3}+2x\); h, \(\frac{x+4}{5}.x+4=\frac{x}{3}-\frac{x-2}{2}\)
i, \(\frac{4x+3}{5}-\frac{6x-2}{7}=\frac{5x+4}{3}+3\); k, \(\frac{5x+2}{6}-\frac{8x-1}{3}=\frac{4x+2}{5}-5\)
m, \(\frac{2x-1}{5}-\frac{x-2}{3}=\frac{x+7}{15}\); n, \(\frac{1}{4}\left(x+3\right)=3-\frac{1}{2}\left(x+1\right).\frac{1}{3}\left(x+2\right)\)
p, \(\frac{x}{3}-\frac{2x+1}{6}=\frac{x}{6}-x\); q, \(\frac{2+x}{5}-0,5x=\frac{1-2x}{4}+0,25\)
r, \(\frac{3x-11}{11}-\frac{x}{3}=\frac{3x-5}{7}-\frac{5x-3}{9}\); s, \(\frac{9x-0,7}{4}-\frac{5x-1,5}{7}=\frac{7x-1,1}{6}-\frac{5\left(0,4-2x\right)}{6}\)
t, \(\frac{2x-8}{6}.\frac{3x+1}{4}=\frac{9x-2}{8}+\frac{3x-1}{12}\); u, \(\frac{x+5}{4}-\frac{2x-3}{3}=\frac{6x-1}{3}+\frac{2x-1}{12}\)
v, \(\frac{5x-1}{10}+\frac{2x+3}{6}=\frac{x-8}{15}-\frac{x}{30}\); w, \(\frac{2x-\frac{4-3x}{5}}{15}=\frac{7x\frac{x-3}{2}}{5}-x+1\)
Đây là những bài cơ bản mà bạn!
\(\frac{5x-2}{3}=\frac{5-3x}{2}\)
\(< =>\frac{\left(5x-2\right).2}{6}=\frac{\left(5-3x\right).3}{6}\)
\(< =>\left(5x-2\right).2=\left(5-3x\right).3\)
\(< =>10x-4=15-9x\)
\(< =>10x+9x=15+4\)
\(< =>19x=19< =>x=1\)
\(\frac{10x+3}{12}=1+\frac{6+8x}{9}\)
\(< =>\frac{\left(10x+3\right).3}{36}=\frac{36}{36}+\frac{\left(6+8x\right).4}{36}\)
\(< =>\left(10x+3\right).3=36+\left(6+8x\right).4\)
\(< =>30x+9=36+24+32x\)
\(< =>32x-30x=9-36-24\)
\(< =>2x=9-60=-51< =>x=-\frac{51}{2}\)
\(2\left(x+\frac{3}{5}\right)=5-\left(\frac{13}{5}+x\right)\)
\(< =>2x+\frac{6}{5}=5-\frac{13}{5}-x\)
\(< =>2x+x=\frac{25}{5}-\frac{13}{5}-\frac{6}{5}\)
\(< =>3x=\frac{25-13-6}{5}=\frac{25-19}{5}\)
\(< =>3x=\frac{6}{5}< =>x=\frac{6}{5}:3=\frac{6}{5.3}=\frac{6}{15}=\frac{2}{5}\)
\(\frac{7}{8}x-5\left(x-9\right)=\frac{20x+1,5}{6}\)
\(< =>\frac{7}{8}x-5x+45=\frac{20x+1,5}{6}\)
\(< =>\frac{7x}{8}-\frac{40x}{8}=\frac{20x+1,5}{6}-\frac{46.6}{6}\)
\(< =>-\frac{33x}{8}=\frac{20x+1,5-276}{6}\)
\(< =>-33x.6=8.\left(20x-274,5\right)\)
\(< =>-198x=160x-2196\)
\(< =>38x=2196< =>x=57,7\)
\(\frac{7x-1}{6}+2x=\frac{16-x}{5}\)
\(< =>\frac{\left(7x-1\right).5}{30}+2x=\frac{\left(16-x\right).6}{30}\)
\(< =>\frac{96-6x}{30}-\frac{35x-5}{30}=2x\)
\(< =>\frac{-41x+101}{30}=2x< =>101x=101\)
\(< =>x=\frac{101}{101}=1\)
\(4.\left(0,5-1,5x\right)=\frac{5x-6}{3}\)
\(< =>2-6x=\frac{5x-6}{3}\)
\(< =>3\left(2-6x\right)=5x-6\)
\(< =>6-18x=5x-6\)
\(< =>12=23x< =>x=\frac{12}{23}\)
\(\frac{3x+2}{2}-\frac{3x+1}{6}=\frac{5}{3}+2x\)
\(< =>\frac{\left(3x+2\right).3}{6}-\frac{3x+1}{6}=\frac{10}{6}+\frac{2x.6}{6}\)
\(< =>\left(3x+2\right).3-\left(3x+1\right)=10+12x\)
\(< =>9x+6-3x-1=10+12x\)
\(< =>6x+5=10+12x\)
\(< =>12x-6x=5-10< =>6x=-5< =>x=-\frac{5}{6}\)
\(\frac{x+4}{5}.x+4=\frac{x}{3}-\frac{x-2}{2}\)
\(< =>\frac{x\left(x+4\right).6}{30}+\frac{4.30}{30}=\frac{x.10}{30}-\frac{\left(x-2\right).15}{30}\)
\(< =>\left(x^2+4x\right).6+120=10x-\left(x-2\right).15\)
\(< =>6x^2+24x+120=10x-15x+30\)
\(< =>6x^2+24x+5x+120-30=0\)
\(< =>6x^2+29x+90=0\)
\(< =>6\left(x^2+2.x.\frac{29}{12}+\frac{29}{12}^2\right)-\frac{29^2.6}{12^2}+90=0\)
\(< =>6\left(x+\frac{29}{12}\right)^2+\frac{90.12^2-29^2.6}{12^2}=0\)
Do \(90.12^2>29^2.6\)=> pt vô nghiệm
\(\frac{4x+3}{5}-\frac{6x-2}{7}=\frac{5x+4}{3}+3\)
\(< =>\frac{4x+3}{5}-\frac{5x+4}{3}=3+\frac{6x-2}{7}\)
\(< =>\frac{\left(4x+3\right).3}{15}-\frac{5\left(5x+4\right)}{15}=\frac{6x-2}{7}+\frac{21}{7}\)
\(< =>\frac{12x+9-25x-20}{15}=\frac{6x+19}{7}\)
\(< =>\left(-13x-11\right).7=\left(6x+19\right).15\)
\(< =>90x+285+91x+77=0\)
\(< =>181x=-362< =>x=-2\)
\(\frac{5x+2}{6}-\frac{8x-1}{3}=\frac{4x+2}{5}-5\)
\(< =>\frac{\left(5x+2\right).5}{30}-\frac{\left(8x-1\right).10}{30}=\frac{\left(4x+2\right).6}{30}-\frac{150}{30}\)
\(< =>\left(5x+2\right).5-\left(8x-1\right).10=\left(4x+2\right).6-150\)
\(< =>25x+10-80x+10=24x+12-150\)
\(< =>24x+55x=20-12+150\)
\(< =>79x=158< =>x=2\)
\(\frac{2x-1}{5}-\frac{x-2}{3}=\frac{x+7}{15}\)
\(< =>\frac{\left(2x-1\right).3}{15}-\frac{\left(x-2\right).5}{15}=\frac{x+7}{15}\)
\(< =>\left(2x-1\right).3-\left(x-2\right).5=x+7\)
\(< =>6x-3-5x+10=x+7\)
\(< =>x-x=7-7< =>0=0\)
=> pt đúng với mọi x
\(\frac{1}{4}.\left(x+3\right)=3-\frac{1}{2}\left(x+1\right)-\frac{1}{3}\left(x+2\right)\)
\(< =>\frac{x}{4}+\frac{3}{4}=3-\frac{1}{2}x-\frac{1}{2}-\frac{1}{3}x-\frac{3}{2}\)
\(< =>\frac{x}{4}+\frac{x}{3}+\frac{x}{2}=3-1-\frac{3}{4}=2-\frac{3}{4}=\frac{5}{4}\)
\(< =>\frac{3x}{12}+\frac{4x}{12}+\frac{6x}{12}=\frac{15}{12}\)
\(< =>3x+4x+6x=15< =>13x=15\)
\(< =>x=\frac{15}{13}\)
\(\frac{x}{3}-\frac{2x+1}{6}=\frac{x}{6}-x\)
\(< =>\frac{2x}{6}-\frac{2x+1}{6}=\frac{x}{6}-\frac{6x}{6}\)
\(< =>2x-\left(2x+1\right)=x-6x\)
\(< =>-1=-5x< =>x=\frac{1}{5}\)
\(\frac{2+x}{5}-0,5x=\frac{1-2x}{4}+0,25\)
\(< =>\frac{2+x}{5}-\frac{x}{2}=\frac{1-2x}{4}+\frac{1}{5}\)
\(< =>\frac{\left(2+x\right).4}{20}-\frac{10.x}{20}=\frac{\left(1-2x\right).5}{20}+\frac{4}{20}\)
\(< =>8+4x-10x=5-10x+4\)
\(< =>4x+8=9< =>4x=1< =>x=\frac{1}{4}\)
\(\frac{3x-11}{11}-\frac{x}{3}=\frac{3x-5}{7}-\frac{5x-3}{9}\)
\(< =>\frac{3x}{11}=1+\frac{21x}{63}+\frac{\left(3x-5\right).9}{63}-\frac{\left(5x-3\right).7}{63}\)
\(< =>\frac{3x}{11}=\frac{63+21x+27x-45-35x+21}{63}\)
\(< =>\frac{3x}{11}=\frac{111x-35x-24}{63}\)
\(< =>\frac{3x}{11}=\frac{76x-24}{63}< =>189x=836x-264\)
\(< =>647x=264< =>x=\frac{264}{647}\)
\(\frac{9x-0,7}{4}-\frac{5x-1,5}{7}=\frac{7x-1,1}{6}-\frac{5\left(0,4-2x\right)}{6}\)
\(< =>\frac{\left(9x-0,7\right).21}{4.21}-\frac{\left(5x-1,5\right).12}{7.12}=\frac{\left(7x-1,1\right).14}{6.14}-\frac{5\left(0,4-2x\right).14}{6.14}\)
\(< =>\frac{189x-8,4}{84}-\frac{60x-18}{84}=\frac{98x-15,4}{84}-\frac{28-140x}{84}\)
\(< =>189x-8,4-60x+18=98x-15,4-28+140x\)
\(< =>129x+9,6=238x-43,4\)
\(< =>109x=9,6+43,4=53\)
\(< =>x=\frac{53}{109}\)
