Giải bất phương trình sau:
a) $\dfrac{3(2x+1)}{20}+1>\dfrac{3x+52}{10}$;
b) $\dfrac{4x-1}{2}+\dfrac{6x-19}{6}\le \dfrac{9x-11}{3}$.
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Bài 1:
a) Ta có: \(2\left(3-4x\right)=10-\left(2x-5\right)\)
\(\Leftrightarrow6-8x-10+2x-5=0\)
\(\Leftrightarrow-6x+11=0\)
\(\Leftrightarrow-6x=-11\)
hay \(x=\dfrac{11}{6}\)
b) Ta có: \(3\left(2-4x\right)=11-\left(3x-1\right)\)
\(\Leftrightarrow6-12x-11+3x-1=0\)
\(\Leftrightarrow-9x-6=0\)
\(\Leftrightarrow-9x=6\)
hay \(x=-\dfrac{2}{3}\)
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ta có:
2x+(2x+1)/2=2x+2x/2+1/2=2x+x+1/2=3x+1/2;
ta có:
2x+(2x+1)/2>3x-1/5
<=>3x+1/2=3x-1/5
<=>1/2>-1/5(luôn đúng)
vậy BPT có vô số nghiệm
a: \(\Leftrightarrow20x^2-12x+15x+5< 10x\left(2x+1\right)-30\)
\(\Leftrightarrow20x^2+3x+5< 20x^2+10x-30\)
=>3x+5<10x-30
=>-7x<-35
hay x>5
b: \(\Leftrightarrow4\left(5x-20\right)-6\left(2x^2+x\right)>4x\left(1-3x\right)-15x\)
\(\Leftrightarrow20x-80-12x^2-6x>4x-12x^2-15x\)
=>14x-80>-11x
=>25x>80
hay x>16/5
\(3x-1\le23\)
\(\Leftrightarrow3x-1+1\le23+1\)
\(\Leftrightarrow3x\le24\)
\(\Leftrightarrow x\le8\)
a,<=>3x<=24
<=>x<=8
Vậy ....
b, <=>4x-8>=9x-3-2x-1
<=>4x-9x+2x>=8-3-1
<=>-3x>=4
<=>x>=-4/3 Vậy ....
a: \(\dfrac{3\left(2x+1\right)}{20}+1>\dfrac{3x+52}{10}\)
=>\(\dfrac{6x+3}{20}+\dfrac{20}{20}>\dfrac{6x+104}{20}\)
=>6x+23>6x+104
=>23>104(sai)
vậy: \(x\in\varnothing\)
b: \(\dfrac{4x-1}{2}+\dfrac{6x-19}{6}< =\dfrac{9x-11}{3}\)
=>\(\dfrac{3\left(4x-1\right)+6x-19}{6}< =\dfrac{2\left(9x-11\right)}{6}\)
=>12x-3+6x-19<=18x-22
=>-22<=-22(luôn đúng)
Vậy: \(x\in R\)