1.
a)
[tex]2.4+1\cfrac{5}{7}*4\cfrac{3}{8}=\cfrac{24}{10}+\cfrac{12}{7}*\cfrac{35}{8}=\cfrac{24}{10}+\cfrac{420}{56}=\cfrac{168}{70}+\cfrac{525}{70}=\cfrac{693}{70}=\cfrac{99}{10}=9.9[/tex]
b)
[tex]\left(2.2+\cfrac{2}{5}\right):\cfrac{1}{2}-3\cfrac{1}{5}=\left(\cfrac{11}{5}+\cfrac{2}{5}\right)*2-\cfrac{16}{5}=\cfrac{13}{5}*2-\cfrac{16}{5}=\cfrac{26}{5}-\cfrac{16}{5}=\cfrac{10}{5}=2[/tex]
c)
[tex]-7*(-3)-27:9=21-3=18[/tex]
d)
[tex]-14:(-7)+54*(-1)*(-2)=2+108=110[/tex]
2.
[tex]-x^2-8xy+2\,,\begin{cases}x=-1\\y=2\end{cases}\\-(-1)^2-8(-1)2+2=-1-(-16)+2=-1+16+2=17[/tex]
3.
a)
[tex]2(x+3y-6)+5(x-2y-1)=2x+6y-12+5x-10y-5=7x-4y-17[/tex]
b)
[tex](4x+3)(x-1)-(2x-3)(x+5)=(4x^2-4x+3x-3)-(2x^2+10x-3x-15)=\\=4x^2-4x+3x-3-2x^2-10x+3x+15=2x^2-8x+12[/tex]
4.
a)
[tex]4x+3=2x-9\\2x=-12\\x=-6[/tex]
b)
[tex]\cfrac{4x-1}{3}=5\\4x-1=15\\4x=16\\x=4[/tex]
c)
[tex](x+2)(x-2)=6x-x^2\\x^2-2^2=6x-x^2\\2x^2-6x-4=0\\x^2-3x-2=0\\\Delta=b^2-4ac=(-3)^2-4*1*(-2)=9+8=17\\x_1=\cfrac{-b-\sqrt\Delta}{2a}=\cfrac{3-\sqrt{17}}{2}\\x_2=\cfrac{-b+\sqrt\Delta}{2a}=\cfrac{3+\sqrt{17}}{2}\\x\in\left\{\cfrac{3-\sqrt{17}}{2},\cfrac{3+\sqrt{17}}{2}\right\}[/tex]
