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a) 0,25x+1,5=0
=> x = (0 - 1,5) : 0,25 = -1,5 : 0,25 = -6
Vậy x = -6.
b) 6,36−5,3x=0
=> x = (0 + 6,36) : 5,3 = 6,36 : 5,3 =\(\dfrac{6}{5}=1,2\)
Vậy x = 1,2.
c) 43x−56=12
=> x = \(\left(\dfrac{1}{2}+\dfrac{5}{6}\right)\): \(\dfrac{4}{3}\) = \(\dfrac{4}{3}:\dfrac{4}{3}=1\)
Vậy x = 1.
d) −59x+1=23x−10
=> \(\dfrac{-5}{9}x-\dfrac{2}{3}x=\dfrac{-11}{9}x=-10-1=-11\)
=> \(x=-11:\dfrac{-11}{9}=9\)
Vậy x = 9.
a) ĐKXĐ: x # -5
\(\dfrac{2x-5}{x+5}=3\) ⇔ \(\dfrac{2x-5}{x+5}=\dfrac{3\left(x+5\right)}{x+5}\)
⇔ 2x - 5 = 3x + 15
⇔ 2x - 3x = 5 + 20
⇔ x = -20 thoả ĐKXĐ
Vậy tập hợp nghiệm S = {-20}
b) ĐKXĐ: x # 0
\(\dfrac{x^2-6}{x}=x+\dfrac{3}{2}\Leftrightarrow\dfrac{2\left(x^2+6\right)}{2x}=\dfrac{2x^2+3x}{2x}\)
Suy ra: 2x2 – 12 = 2x2 + 3x ⇔ 3x = -12 ⇔ x = -4 thoả x # 0
Vậy tập hợp nghiệm S = {-4}.
c) ĐKXĐ: x # 3
\(\dfrac{\left(x^2+2x\right)-\left(3x+6\right)}{x-3}=0\) ⇔ x(x + 2) - 3(x + 2) = 0
⇔ (x - 3)(x + 2) = 0 mà x # 3
⇔ x + 2 = 0
⇔ x = -2
Vậy tập hợp nghiệm S = {-2}
d) ĐKXĐ: x # \(-\dfrac{2}{3}\)
\(\dfrac{5}{3x+2}=2x-1\Leftrightarrow\dfrac{5}{3x+2}=\dfrac{\left(2x-1\right)\left(3x+2\right)}{3x+2}\)
⇔ 5 = (2x - 1)(3x + 2)
⇔ 6x2 – 3x + 4x – 2 – 5 = 0
⇔ 6x2 + x - 7 = 0
⇔ 6x2 - 6x + 7x - 7 = 0
⇔ 6x(x - 1) + 7(x - 1) = 0
⇔ (6x + 7)(x - 1) = 0
⇔ x = \(-\dfrac{7}{6}\) hoặc x = 1 thoả x # \(-\dfrac{2}{3}\)
Vậy tập nghiệm S = {1;\(-\dfrac{7}{6}\)}.
a)ĐKXĐ:x≠-5
Khử mẫu:2x-5=3(x+5) (1)
giải phương trình (1),ta được:
(1)⇔2x-5=3x+15
⇔2x-3x=15+5
⇔-x=20⇔x=-20(TM)
vậy phương trình đã cho có nghiệm x=-20
giải các phương trình sau:
a) 6x-3= 4x+5
b) \(\dfrac{2x+3}{x+1}\)- \(\dfrac{6}{x}\)= 2
c) \(|3x-1|\)=3x
a)\(6x-3=4x+5\)
\(\Rightarrow6x-3-4x-5=0\)
\(\Rightarrow2x-8=0\)
\(\Rightarrow x=4\)
Vậy x=4
b)\(\frac{2x+3}{x+1}-\frac{6}{x}=2\left(ĐKXĐ:x\ne-1;0\right)\)
\(\Rightarrow\frac{2x^2+3x}{x\left(x+1\right)}-\frac{6x+6}{x\left(x+1\right)}=2\)
\(\Rightarrow\frac{2x^2+3x-6x-6}{x\left(x+1\right)}=2\)
\(\Rightarrow2x^2-3x-6=2\left(x^2+x\right)\)
\(\Rightarrow2x^2-3x-6-2x^2-2x=0\)
\(\Rightarrow-5x-6=0\)
\(\Rightarrow x=-\frac{6}{5}\)
Vậy \(x=-\frac{6}{5}\)
c)\(\left|3x-1\right|=3x\left(1\right)\)
TH1:\(x\ge\frac{1}{3}\).PT(1) có dạng:3x-1=3x
0x=1
PT vô nghiệm
TH2:\(x< \frac{1}{3}\).PT(1) có dạng:1-3x=3x
\(\Rightarrow6x=1\)
\(\Rightarrow x=\frac{1}{6}\left(TM\right)\)
Vậy PT có nghiệm là \(\frac{1}{6}\)
a, \(6x-3=4x+5 \)
\(\Leftrightarrow6x-4x=5+3\)
\(\Leftrightarrow2x=8\)
\(\Leftrightarrow x=4\)
vậy no của pt là : x = 4
b, \(\frac{2x+3}{x+1}-\frac{6}{x}=2\)
ĐKXĐ : \(\hept{\begin{cases}x\ne-1\\x\ne0\end{cases}}\)
\(\Leftrightarrow\frac{2x^2+3x-6x-6}{x\left(x+1\right)}=2\)
\(\Leftrightarrow\frac{2x^2-3x-6}{x\left(x+1\right)}=2\)
\(\Leftrightarrow2x^2-3x-6=2x^2+2x\)
\(\Leftrightarrow-5x=6\)
\(\Leftrightarrow x=\frac{-6}{5}\)
vậy no của pt là x=-6/5
c, \(\left|3x-1\right|=3x\)
Với \(3x-1\ge0\)
\(\Rightarrow3x-1=3x\Leftrightarrow-1=0\)( vô lí )
a: \(\Leftrightarrow-12x-4=8x-2-8-6x\)
=>-12x-4=2x-10
=>-14x=-6
hay x=3/7
b: \(\Leftrightarrow3\left(5x-3\right)-2\left(5x-1\right)=-4\)
=>15x-9-10x+2=-4
=>5x-7=-4
=>5x=3
hay x=3/5(loại)
c: \(\Leftrightarrow x^2-4+3x+3=3+x^2-x-2\)
\(\Leftrightarrow x^2+3x-1=x^2-x+1\)
=>4x=2
hay x=1/2(nhận)
1)\(-\dfrac{4x-3}{x-5}=\dfrac{29}{3}\Leftrightarrow\dfrac{3-4x}{x-5}=\dfrac{29}{3}\)
\(\Leftrightarrow3\left(3-4x\right)=29\left(x-5\right)\Leftrightarrow9-12x=29x-145\)
\(\Leftrightarrow29x+12x=9+145\Leftrightarrow41x=154\Leftrightarrow x=\dfrac{154}{41}\)
2)\(\dfrac{2x-1}{5-3x}=2\Leftrightarrow2\left(2x-1\right)=5-3x\)
\(\Leftrightarrow4x-2=5-3x\)
\(\Leftrightarrow4x+3x=5+2\Leftrightarrow7x=7\Leftrightarrow x=1\)
3)\(\dfrac{4x-5}{x-1}=2+\dfrac{x}{x-1}\)
\(\Leftrightarrow\dfrac{4x-5}{x-1}=\dfrac{2\left(x-1\right)}{x-1}+\dfrac{x}{x-1}\)
\(\Rightarrow4x-5=2x-2+x\)
\(\Leftrightarrow4x-2x-x=-2+5\)
\(\Leftrightarrow x=3\)
\(1)-\dfrac{4x-3}{x-5}=\dfrac{29}{3} (x \neq 5) \\\Leftrightarrow\dfrac{3-4x}{x-5}=\dfrac{29}{3}\) \(\Leftrightarrow3\left(3-4x\right)=29\left(x-5\right)\\\Leftrightarrow9-12x=29x-145\) \(\Leftrightarrow29x+12x=9+145\\\Leftrightarrow41x=154\\\Leftrightarrow x=\dfrac{154}{41}(TM)\)
Vậy \(S=\left\{\dfrac{154}{41}\right\}\)
\(2)\dfrac{2x-1}{5-3x}=2 (x \neq \dfrac{5}{3}) \)
\(\Leftrightarrow2x-1=2\left(5-3x\right)\\ \Leftrightarrow2x-1=10-6x\\ \Leftrightarrow2x+6x=10+1\\ \Leftrightarrow8x=11\\ \Leftrightarrow x=\dfrac{11}{8}\left(TM\right)\)
Vậy \(S=\left\{\dfrac{11}{8}\right\}\)
\(3)\dfrac{4x-5}{x-1}=2+\dfrac{x}{x-1} (x \neq 1) \\\Leftrightarrow\dfrac{4x-5}{x-1}=\dfrac{2\left(x-1\right)}{x-1}+\dfrac{x}{x-1}\) \(\Leftrightarrow4x-5=2x-2+x\) \(\Leftrightarrow4x-2x-x=-2+5\) \(\Leftrightarrow x=3(TM)\)
Vậy \(S=\left\{3\right\}\)
a) \(\left(4x-10\right)\left(24+5x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}4x-10=0\\24+5x=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{10}{4}=\dfrac{5}{2}\\x=-\dfrac{24}{5}\end{matrix}\right.\)
Vậy \(S=\left\{-\dfrac{24}{5};\dfrac{5}{2}\right\}\)
b) \(\left(3.5-7x\right)\left(0.1x+2.3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}3.5-7x=0\\0.1x+2.3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{3.5}{7}=\dfrac{1}{2}\\x=-\dfrac{2.3}{0.1}=-23\end{matrix}\right.\)
Vậy \(S=\left\{-23;\dfrac{1}{2}\right\}\)
c: =>|x-2|+3=-5 hoặc |x-2|+3=5
=>|x-2|=2
=>x-2=2 hoặc x-2=-2
=>x=4 hoặc x=0
ĐKXĐ : \(\left\{{}\begin{matrix}x\ne2\\x\ne\dfrac{3}{4}\end{matrix}\right.\)
PT \(\Leftrightarrow\dfrac{5\left(3-4x\right)+6\left(x-2\right)}{\left(x-2\right)\left(3-4x\right)}=0\)
\(\Leftrightarrow5\left(3-4x\right)+6\left(x-2\right)=0\)
\(\Leftrightarrow15-20x+6x-12=0\)
\(\Leftrightarrow-14x+3=0\)
\(\Leftrightarrow x=\dfrac{3}{14}\)
Vậy ...