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\(\left(x-1\right)\left(x+1\right)-2\left(2x+3\right)\le\left(x-2\right)^2+x\)
\(\Leftrightarrow x^2-1-4x-6\le x^2-4x+4+x\)
\(\Leftrightarrow x^2-4x-7\le x^2-3x+4\)
\(\Leftrightarrow x^2-4x-x^2+3x\le7+4\)
\(\Leftrightarrow-x\le11\)
\(\Leftrightarrow x\le-11\)
Cho x,y,z là các sô dương.Chứng minh rằng x/2x+y+z+y/2y+z+x+z/2z+x+y<=3/4
\(\frac{25x-655}{95}-\frac{5\left(x-12\right)}{209}=\frac{89-3x-\frac{2\left(x-18\right)}{5}}{11}\)
\(< =>\frac{5x-131}{19}=\frac{1631-52x-\frac{38x-684}{5}}{209}\)
\(< =>\left(5x-131\right)209=\left(1631-52x-\frac{38x-684}{5}\right)19\)
\(< =>55x-1441=1631-52x-\frac{38x-684}{5}\)
\(< =>3072-107x=\frac{38x-684}{5}\)
\(< =>\left(3072-107x\right)5=38x-684\)
\(< =>15360-535x-38x-684=0\)
\(< =>14676=573x< =>x=\frac{14676}{573}=\frac{4892}{191}\)
nghệm xấu thế
\(\frac{8\left(x+22\right)}{45}-\frac{7x+149+\frac{6\left(x+12\right)}{5}}{9}=\frac{x+35+\frac{2\left(x+50\right)}{9}}{5}\)
\(< =>\frac{8x+176}{45}-\frac{41x+817}{45}=\frac{11x+415}{45}\)
\(< =>993-33x-11x-415=0\)
\(< =>578=44x< =>x=\frac{289}{22}\)
Giải phương trình và bất phương trình
a)\(\frac{2x-1}{6}-x-3=\frac{3-2\left(x+5\right)}{4}\)
<=>\(\frac{2\left(2x-1\right)}{12}-\frac{12x}{12}-\frac{36}{12}=\frac{9-6\left(x+5\right)}{12}\)
<=>4x-2-12x-36=9-6x-30
<=>-2x= 17
<=>x=-8,5
Vậy S={-8,5}
b)\(\left|x-4\right|+3=-3x-21\)(*)
Ta có |x-4|=x-4 khi x-4≥0 <=> x≥4
khi đó (*) tạo thành x-4+3=-3x-21
<=>4x=-20
<=>x=-5(ktm)
Ta có |x-4|=-x+4 khi x-4<0<=>x<4
Khi đó (*) tạo thành -x+4+3=-3x-21
<=>2x=-28
<=>x=-14(tm)
vậy S={-14}
c)\(\frac{x-1}{2}-\frac{x-2}{3}lớnhonhoac=x-\frac{x-3}{4}\)
<=>\(\frac{6\left(x-1\right)}{12}-\frac{4\left(x-2\right)}{12}lonhonhoacbang\:\frac{12x}{12}-\frac{3\left(x-3\right)}{12}\)
<=>6x-6-4x+8≥12x-3x+9
<=>-7x≥7
<=>x≤-1
Vậy S={x/x≤-1}
a, \(\frac{\left(x-2\right)^2}{3}-\frac{\left(2x-3\right).\left(2x+3\right)}{8}+\frac{\left(x-4\right)^2}{6}=0\)
\(\Leftrightarrow\frac{x^2-4x+4}{3}+\frac{9-4x^2}{8}+\frac{x^2-8x+16}{6}=0\)
\(\Leftrightarrow\frac{8\left(x^2-4x+4\right)+3\left(9-4x^2\right)+4\left(x^2-8x+16\right)}{24}=0\)
\(\Leftrightarrow\frac{8x^2-32x+32+27-12x^2+4x^2-32x+64}{24}=0\)
\(\Leftrightarrow\frac{123-64x}{24}=0\Leftrightarrow123-64x=0\Leftrightarrow x=\frac{123}{64}\)
\(2+\frac{3\left(x+1\right)}{8}< 3-\frac{x-1}{4}\)
<=> \(2+\frac{3}{8}x+\frac{3}{8}< 3-\frac{1}{4}x+\frac{1}{4}\)
<=> \(\frac{3}{8}x+\frac{1}{4}x< 3+\frac{1}{4}-2-\frac{3}{8}\)
<=> \(\frac{5}{8}x< \frac{7}{8}\)
<=> x < 7/5
Vậy bpt có tập nghiệm { x | x < 7/5 }
\(\frac{2x+1}{4}-1\ge\frac{3x-1}{3}\)
<=> \(\frac{1}{2}x+\frac{1}{4}-1\ge x-\frac{1}{3}\)
<=> \(\frac{1}{2}x-x\ge-\frac{1}{3}-\frac{1}{4}+1\)
<=> \(-\frac{1}{2}x\ge\frac{5}{12}\)
<=> \(x\le-\frac{5}{6}\)
Vậy bpt có tập nghiệm { x | x ≤ -5/6 }
a, \(2+\frac{3\left(x+1\right)}{8}< 3-\frac{x-1}{4}\)
\(\Leftrightarrow\frac{16+3x+3}{8}< \frac{12-x+1}{4}=\frac{26-2x}{8}\)
\(\Rightarrow19+3x< 26-2x\Rightarrow-7< -5x\Rightarrow x< \frac{7}{5}\)
b, \(\frac{2x+1}{4}-1\ge\frac{3x-1}{3}\Leftrightarrow\frac{6x+3-12}{12}\ge\frac{12x-4}{12}\)
\(\Rightarrow6x-9\ge12x-4\Rightarrow-6x-5\ge0\Rightarrow x\le-\frac{5}{6}\)