1.
[tex](3x-4)(2x-1)=(6x+2)(x-1)\\\\x^{2} -3x -8x+4 =6x^{2} -6x +2x -2\\6=6x^{2}-6x+2x-6x^{2}+3x+8x\\6=7x\\x=\frac{6}{7}[/tex]
2.
[tex](9x+1)(2x-1)=(1-6x)(1-3x)\\18x^{2}-9x +2x-1=1-3x-6x+18x^{2} \\18x^{2} -18x^{2} -9x+2x+6x+3=1+1\\2x=2\\x=1[/tex]
3.
[tex]9x^{2} -(3-4x)(3-2x)<x(x-9)\\9x^{2} +(-3+4x)(3-2x)<x(x-9)\\9x^{2}-8x^{2} +6x+12x-9<x^{2} -9x\\x^{2} +18x-9<x^{2} -9x\\27x<9\\x=\frac{1}{3}[/tex]
4.
[tex](x+1\frac{1}{2} )(2x+1)\geq (2x+\frac{1}{2} )(x-1)+6x\\2x^{2} +x+3x+\frac{3}{2} \geq 2x^{2} -2x+\frac{1}{2}x-\frac{1}{2}+6x \\2x^{2} -2x^{2} +x+3x+2x-\frac{1}{2} x -6x\geq -\frac{3}{2}-\frac{1}{2} \\-\frac{1}{2}x\geq -\frac{4}{2} \\x\leq 4[/tex]
