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a)\(\frac{3x}{7}=\frac{5x-1}{2}=>\frac{6x}{14}=\frac{35x-7}{14}\)
=>6x=35x-7
=>35x-6x=7
=>29x=7
=>\(x=\frac{7}{29}\)
b)\(\frac{2-5x}{3}=\frac{4+x}{5}=>\frac{10-25x}{15}=\frac{12+3x}{15}\)
=>10-25x=12+3x
=>25x+3x=10-12
=>28x=-2
=>\(x=\frac{-2}{28}=-\frac{1}{14}\)
\(\frac{3x+2}{5x+7}=\frac{3x-1}{5x+1}\)
\(\Rightarrow\left(3x+2\right)\left(5x+1\right)=\left(3x-1\right)\left(5x+7\right)\)
\(\Rightarrow15x^2+10x+3x+2=15x^2-5x+21x-7\)
\(3x=9\)
\(x=3\)
Ta có: (3x+2)(5x+1)=(5x+7)(3x-1) (ĐKXĐ: x khác -7/5, x khác -1/5)
=> 15x2+13x+2=15x2+16x-7
=> 3x-9=0 =>x=3 (chọn)
a) 2|2/3 - x| = 1/2
|2/3 - x| = 1/4
|2/3 - x| = 1/4 hoặc |2/3 - x| = -1/4
Xét 2 TH...
a) \(\frac{2x+3}{5x+2}=\frac{4x+5}{10x+2}\)
\(\Leftrightarrow\)\(\left(2x+3\right)\left(10x+2\right)=\left(5x+2\right)\left(4x+5\right)\)
\(\Leftrightarrow20x^2+4x+30x+6=20x^2+25x+8x+10\)
\(\Leftrightarrow20x^2-20x^2+4x+30x-25x-8x=10-6\)
\(\Leftrightarrow x=4\)
b) \(\frac{3x-1}{40-5x}=\frac{25-3x}{5x-34}\)
\(\Leftrightarrow\left(3x-1\right)\left(5x-34\right)=\left(40-5x\right)\left(25-3x\right)\)
\(\Leftrightarrow15x^2-102x-5x+34=1000-120x-125x+15x^2\)
\(\Leftrightarrow15x^2-15x^2-102x-5x+120x+125x=1000-34\)
\(\Leftrightarrow138x=966\)
\(\Leftrightarrow x=7\)
a ) \(\frac{2x+3}{5x+2}=\frac{4x+5}{10x+2}\)
\(\left(2x+3\right).\left(10x+2\right)=\left(5x+2\right)\left(4x+5\right)\)
\(20x^2+4x+30x+6=20x^2+25x+8x+10\)
\(4x+30x-25x-8x=10-6\)
\(x=4\)
Áp dụng tính chất của dãy tỉ số bằng nhau ta có:
\(\frac{2x+3}{5x+2}=\frac{4x+5}{10x+2}=\frac{2.\left(2x+3\right)-\left(4x+5\right)}{2.\left(5x+2\right)-\left(10x+2\right)}=\frac{4x+6-4x-5}{10x+4-10x-2}=\frac{1}{2}\)
Suy ra:
\(\frac{2x+3}{5x+2}=\frac{1}{2}\Rightarrow2.\left(2x+3\right)=1.\left(5x+2\right)\Rightarrow4x+6=5x+2\)
\(\Rightarrow x=4\)
\(\Rightarrow\left(5x-2\right)\left(6x-2\right)=\left(3x+1\right).13\)
\(\Leftrightarrow30x^2-10x-12x+4=39x+13\)
\(\Leftrightarrow30x^2-61x-9=0\)
a)\(\left(\frac{4}{5}\right)^{2x+7}=\left(\frac{4}{5}\right)^4\)
=> 2x + 7 = 4
2x = 4 - 7
2x = -3
x = -3 : 2
x = -1,5
Vậy x = -1,5
a) \(\frac{6x-5}{-7}=\frac{5x-3}{-5}\)
=> -5(6x - 5) = -7(5x - 3)
=> -30x + 25 = -35x + 21
=> -30x + 25 + 35x - 21 = 0
=> (-30x + 35x) + (25 - 21) = 0
=> 5x + 4 = 0
=> 5x = -4
=> x = -4/5
b) \(\frac{12-7x}{-13}=\frac{4-3x}{-5}\)
=> -5(12 - 7x) = -13(4 - 3x)
=> -60 + 35x = -52 + 39x
=> -60 + 35x + 52 - 39x = 0
=> (-60 + 52) + (35x - 39x) = 0
=> -8 - 4x = 0
=> -8 = 4x
=> x = -2
c) \(\frac{2x+4}{7}=\frac{4x-2}{15}\)
=> 15(2x + 4) = 7(4x - 2)
=> 30x + 60 = 28x - 14
=> 30x + 60 - 28x + 14 = 0
=> 2x + 74 = 0
=> 2x = -74
=> x = -37
b) \(\left(5x-1\right)\left(2x-\frac{1}{3}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}5x-1=0\\2x-\frac{1}{3}=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}5x=1\\2x=\frac{1}{3}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{1}{5}\\x=\frac{1}{6}\end{matrix}\right.\)
e, \(-\frac{3}{4}-\left|\frac{4}{5}-x\right|=-1\)
\(\Leftrightarrow\left|\frac{4}{5}-x\right|=-\frac{3}{4}-\left(-1\right)\)
\(\Leftrightarrow\left|\frac{4}{5}-x\right|=\frac{1}{4}\)
\(\Leftrightarrow\left[{}\begin{matrix}\frac{4}{5}-x=\frac{1}{4}\\\frac{4}{5}-x=-\frac{1}{4}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{7}{15}\\x=1,05\end{matrix}\right.\)
Vậy ....
Trả lời:
\(\frac{3x+2}{5x+7}=\frac{2}{3}\)
\(\Rightarrow3\left(3x+2\right)=2\left(5x+7\right)\)
\(\Rightarrow9x+6=10x+14\)
\(\Rightarrow9x-10x=14-6\)
\(\Rightarrow-x=8\)
\(\Rightarrow x=-8\)
Vậy x = - 8
\(\frac{3x+2}{5x+7}\)= \(\frac{2}{3}\)
\(\frac{3x}{5x}\)= \(\frac{2}{3}\)- \(\frac{2}{7}\)
\(\frac{3x}{5x}\)= \(\frac{4}{7}\)
\(\frac{x}{x}\)= \(\frac{4}{7}\): \(\frac{3}{5}\)
\(\frac{x}{x}\)= \(\frac{20}{21}\)