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\(a,4x-6< 7x-12\)
\(\Leftrightarrow6< 3x\Leftrightarrow x>2\)
\(b,\frac{3x-7}{4}\ge2-\frac{x+5}{3}\)
\(\Leftrightarrow3\left(3x-7\right)\ge24-4\left(x+5\right)\)
\(\Leftrightarrow13x\ge25\Leftrightarrow x\ge\frac{25}{13}\)
\(c,\frac{3x-8}{-7}\ge1-\frac{x+2}{-3}\)
\(\Leftrightarrow-3\left(3x-8\right)\ge21+7\left(x+2\right)\)
\(\Leftrightarrow-16x\ge11\)
\(\Leftrightarrow x\le-\frac{11}{16}\)
\(d,-12-8x>3+2x-\left(5-7x\right)\)
\(\Leftrightarrow14>17x\Leftrightarrow x< \frac{14}{17}\)
\(e,-1+\frac{x-1}{-3}\le\frac{x+2}{-9}\)
\(\Leftrightarrow-9-3\left(x-1\right)\le-\left(x+2\right)\)
\(\Leftrightarrow-2x\le4\Leftrightarrow x\ge-2\)
\(\frac{5x-3}{6}-\frac{7x-1}{4}-\frac{4x+2}{7}+5=0\)
<=> \(\frac{14\left(5x-3\right)-21\left(7x-1\right)-12\left(4x+2\right)+420}{84}=0\)
<=> 70x - 42 - 147x + 21 - 48x -24 + 420 = 0
<=> -125x + 375 = 0
<=> -125x = -375
<=> x = 3
Vậy S = {3}
\(\frac{3\left(2x+1\right)}{4}-5-\frac{3x+2}{10}=\frac{2\left(3x-1\right)}{5}\)
<=> \(\frac{15\left(2x+1\right)-100-2\left(3x+2\right)}{20}=\frac{8\left(3x-1\right)}{20}\)
<=> 30x + 15 - 100 - 6x - 4 = 24x - 8
<=> 24x - 24x = -8 + 89
<=> 0x = 81
=> pt vô nghiệm
\(\Leftrightarrow\frac{5\left(x+5\right)-3\left(x-3\right)}{15}=\frac{5\left(x+5\right)-3\left(x-3\right)}{\left(x-3\right)\left(x+5\right)}\)
\(\Leftrightarrow\frac{2x+34}{15}=\frac{2x+34}{x^2+2x-15}\Leftrightarrow\orbr{\begin{cases}2x+34=0\\x^2+2x-15=15\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=-17\\x^2+2x-30=0\end{cases}}\)
Từ đó tìm được \(S=\left\{-17;\sqrt{31}-1;-\sqrt{31}-1\right\}\)
còn đây là câu b
\(\frac{3x-2-30}{6}=\frac{3-2x-14}{4}\)
\(\Leftrightarrow\frac{3x-32}{6}-\frac{-11-2x}{4}=0\)
\(\Leftrightarrow\frac{6x-64+33+6x}{12}\)
\(\Leftrightarrow12x=31\)
\(\Leftrightarrow x=\frac{31}{12}\)
Ta có \(\frac{7x-5}{8}=\frac{3x+1}{5}\)
<=> \(35x-25=24x+8\)
<=> \(35x-24x=8+25\)
<=> \(11x=33\)
<=> x=3
Vậy phương trình có ngiệm duy nhất x=3
\(\frac{7x-5}{8}=\frac{3x+1}{5}\) MTC= 40
\(5\left(7x-5\right)=8\left(3x+1\right)\)
\(35x-25=24x+8\)
\(35x-24x=8+25\)
\(11x=33\)
\(\Rightarrow x=3\)