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a) x^2 +3x-2x-6=0
x^2 + x = 6
x^2 + 0.5x + 0.5x = 6
x (x + 0.5) + 0.5 (x + 0.5) =5.75
(x+0.5)^2 = 5.75
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1+5+9+15+20+32+18+53+21+6=x+216
180=x+216
x+216=180
x=180-216
x=-36
vậy x=-36
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c , d giải nốt:
c) 2x + 3/6 = 7x - 13/15
=> (2x + 3) . 15 = (7x - 13) x 6
=> 30x +45 = 42x - 78
=> 30x - 42x = -78 - 45
=> -12x = -123
=> x = 41/4
d) 2-x/4 = 3x - 1/ - 3
=> (2-x) . -3 = 4. (3x - 1)
=> -6 - (-3x) = 12x - 4
(-6) + 4 = 12x - - (-3x)
=> -2 = 9x
=> x = -2/9
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\(a,\left|x\right|=15-5=10\Leftrightarrow\orbr{\begin{cases}x=10\\x=-10\end{cases}}\)
\(b,\left|x-2\right|+3x=7\)
*) Với x<2\(pt\Leftrightarrow2-x+3x=7\Leftrightarrow2x=5\Leftrightarrow x=\frac{5}{2}\)(loại )
*) Với \(x\ge2\Leftrightarrow x-2+3x=7\)\(\Leftrightarrow4x=9\Leftrightarrow x=\frac{9}{4}\)(thỏa mãn x>=2)
\(c,\left|x-1\right|+2x=6\)
*) Với x<1\(pt\Leftrightarrow1-x+2x=6\Leftrightarrow x=5\)(loại)
*) Với\(x\ge1\Leftrightarrow x-1+2x=6\Leftrightarrow3x=5\)\(\Leftrightarrow x=\frac{5}{3}\)(thỏa mãn x>=1)
\(\text{a)}\left|x\right|+5=15\)
\(\Rightarrow\left|x\right|=10\)
\(\Rightarrow x=10\text{ hay }x=-10\)
\(\text{b)}\left|x-2\right|+3x=7\)
\(\Rightarrow\left|x-2\right|=7-3x\)
\(\text{TH1:}x-2\ge0\Rightarrow x\ge2\)
\(\Rightarrow x-2=7-3x\)
\(\Rightarrow x+3x=7+2\)
\(\Rightarrow4x=9\)
\(\Rightarrow x=\frac{9}{4}\left(\text{Nhận}\right)\)
\(\text{TH2:}x-2< 0\Rightarrow x< 2\)
\(\Rightarrow x-2=-\left(7-3x\right)\)
\(\Rightarrow x-2=-7+3x\)
\(\Rightarrow x-3x=-7+2\)
\(\Rightarrow-2x=-5\)
\(\Rightarrow x=\frac{5}{2}\left(\text{Loại}\right)\)
Vậy \(x=\frac{9}{4}\)
\(\text{c)}\left|x-1\right|+2x=6\)
\(\Rightarrow\left|x-1\right|=6-2x\)
\(\text{TH1:}x-1\ge0\Rightarrow x\ge1\)
\(\Rightarrow x-1=6-2x\)
\(\Rightarrow x+2x=6+1\)
\(\Rightarrow3x=7\)
\(\Rightarrow x=\frac{7}{3}\left(\text{Nhận}\right)\)
\(\text{TH2:}x-2< 0\Rightarrow x< 2\)
\(\Rightarrow x-1=-\left(6-2x\right)\)
\(\Rightarrow x-1=-6+2x\)
\(\Rightarrow x-2x=-6+1\)
\(\Rightarrow-x=-5\)
\(\Rightarrow x=5\left(\text{loại}\right)\)
Vậy \(x=\frac{7}{3}\)
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\(a,2^{x+1}=3^y=12^x\Rightarrow2^{x+1}.3^y=2^{2x}.3y\)
\(\Rightarrow\frac{2^x}{2^{x+1}}=\frac{3^y}{3^x}\Rightarrow2^{2-x-x-1}=3^{y-x}\)
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a. \(x=\dfrac{-2}{15}-\dfrac{3}{10}\)
\(x=\dfrac{-13}{30}\)
b. \(\dfrac{-11}{12}x+\dfrac{1}{4}=\dfrac{5}{6}\)
\(\dfrac{-11}{12}x=\dfrac{5}{6}-\dfrac{1}{4}\)
\(\dfrac{-11}{12}x=\dfrac{7}{12}\)
\(x=\dfrac{7}{12}:\dfrac{-11}{12}\)
\(x=\dfrac{-7}{11}\)
c:=>2003x+2005003=2004
=>2003x=-2002999
hay \(x\in\varnothing\)