1. [tex]4x+(5x+3)=(4x+5x)+3=9x+3[/tex] -- associative property of addition ([tex]a+(b+c)=(a+b)+c[/tex]);
2. [tex]5\cdot (3\cdot 8)=(5\cdot 3)\cdot 8=15\cdot 8[/tex] -- associative property of multiplication ([tex](a\cdot b)\cdot c=a\cdot (b\cdot c)[/tex]);
3. [tex]\dfrac{1}{5}\cdot 5=1[/tex] -- multiplicative inverses ([tex]a\cdot a^{-1}=a^{-1}\cdot a=1[/tex]);
4. a+b=b+a -- commutative addition
5. a+b=b+a=0 -- additive inverses
