[tex]a)\\\\x+5<-3x+2(x-1) \\\\x+5<-3x+2 x-2\\\\x+5<-x-2\\\\x+x<-2-5\\\\2x<-7\ \ |:2\\\\x<-\frac{7}{2}\\\\x\in(-\infty ,-\frac{7}{2})[/tex]
[tex]b)\\\\6-3x<5-4x \\\\-3x+4x<5-6\\\\x<-1\\\\x\in(-\infty ,-1)[/tex]
[tex]c)\\\\ \frac{1}{2}( x+2) \geq 4x+2(x-1) \\\\\frac{1}{2}x+1\geq 4x+2x-2\\\\\frac{1}{2}x+1\geq 6x-2\\\\\frac{1}{2}x-6x\geq -2-1\\\\-5\frac{1}{2}x \geq -3\\\\- \frac{11}{2}x \geq -3\ \ |* (-\frac{2}{11}) \\\\x\leq \frac{6}{11}\\\\x\in(-\infty ,\frac{6}{11}>[/tex]
[tex]d)\\\\ \frac{3}{4}( x-1 )\leq 2x+1\ \ |*4\\\\3(x-1) \leq 8x+4 \\\\3 x-3 \leq 8x+4\\\\3x-8x\leq 4+3\\\\ -5x\leq 7\ \ |-5)\\\\x\geq -\frac{7}{5}\\\\x\in<-\frac{7}{5 } ,+\infty )[/tex]
[tex]e)\\\\-2 (x-1) > 3 ( x+7 )+3 \\\\-2 x+2 > 3x+21+3 \\\\-2x-3x>24-2\\\\-5x>22\ \ |-5)\\\\x<-\frac{22}{5}\\\\x\in(-\infty ,-\frac{22}{5})[/tex]
