Odpowiedź:
[tex]a)\\\\3x^2>16(x-1)\\\\3x^2>16x-16\\\\3x^2-16x+16>0\\\\3x^2-4x-12x+16>0\\\\x(3x-4)-4(3x-4)>0\\\\(3x-4)(x-4)>0\\\\3x-4=0\ \ \ \ \vee\ \ \ \ x-4=0\\\\3x=4\ \ /:3\ \ \vee\ \ \ \ x=4\\\\x=\frac{4}{3}\ \ \ \ \ \ \ \ \ \ \vee\ \ \ \ x=4\\\\x=1\frac{1}{3}\ \ \ \ \ \ \ \ \vee\ \ \ \ x=4[/tex]
[tex]b)\\\\x(7x+2)<7x+2\\\\x(7x+2)-(7x+2)<0\\\\(7x+2)(x-1)<0\\\\7x+2=0\ \ \ \ \ \ \ \ \vee\ \ \ \ x-1=0\\\\7x=-2\ \ /:7\ \ \ \ \vee\ \ \ \ x=1\\\\x=-\frac{2}{7}\ \ \ \ \ \ \ \ \ \ \ \ \vee\ \ \ \ x=1\\\\\\c)\\\\x^2-4x>2x^2-6x\\\\x^2-4x-2x^2+6x>0\\\\-x^2+2x>0\ \ /\cdot(-1)\\\\x^2-2x<0\\\\x(x-2)<0\\\\x=0\ \ \ \ \vee\ \ \ \ x-2=0\\\\x=0\ \ \ \ \vee\ \ \ \ x=2[/tex]
[tex]d)\\\\-4x^2\leq 3-13x\\\\-4x^2-3+13x\leq 0\\\\-4x^2+13x-3\leq 0\ \ /\cdot(-1)\\\\4x^2-13x+3\geq 0\\\\4x^2-12x-x+3\geq 0\\\\4x(x-3)-(x-3)\geq 0\\\\(x-3)(4x-1)\geq 0\\\\x-3=0\ \ \ \ \vee\ \ \ \ 4x-1=0\\\\x=3\ \ \ \ \ \ \ \ \vee\ \ \ \ 4x=1\ \ /:4\\\\x=3\ \ \ \ \ \ \ \ \vee\ \ \ \ x=\frac{1}{4}[/tex]
[tex]e)\\\\(x-2)^2-7\geq 2x^2\\\\x^2-4x+4-7\geq 2x^2\\\\x^2-4x-3-2x^2\geq 0\\\\-x^2-4x-3\geq 0\ \ /\cdot(-1)\\\\x^2+4x+3\leq 0\\\\x^2+x+3x+3\leq 0\\\\x(x+1)+3(x+1)\leq 0\\\\(x+1)(x+3)\leq 0\\\\x+1=0\ \ \ \ \vee\ \ \ \ x+3=0\\\\x=-1\ \ \ \ \ \ \vee\ \ \ \ x=-3[/tex]
[tex]f)\\\\-2x^2-2x+12<0\ \ /:(-2)\\\\x^2+x-6>0\\\\x^2+3x-2x-6>0\\\\x(x+3)-2(x+3)>0\\\\(x+3)(x-2)>0\\\\x+3=0\ \ \ \ \vee\ \ \ \ x-2=0\\\\x=-3\ \ \ \ \ \ \vee\ \ \ \ x=2[/tex]
