class 9th math 2.2 solution

\[\begin{align}
   \left( \text{i} \right)\qquad&a+b=b+a\qquad &&\text{Commutative Property w}\text{.r}\text{.t}\text{. addition } \\
  \left( \text{ii} \right) \qquad &\left( ab \right)c=a\left( bc \right) \qquad &&\text{Associatve Property w}\text{.r}\text{.t}\text{. multiplication} \\
  \left( \text{iii} \right) \qquad &7\times 1=7\qquad &&\text{Multiplicative Identity} \\
  \left( \text{iv} \right) \qquad &x>y\text{ or }x=y\text{ or }x<y\qquad &&\text{Trichotomy Property} \\
  \left( \text{v} \right) \qquad &ab=ba\qquad &&\text{Commutative Property w}\text{.r}\text{.t}\text{. multiplication } \\
  \left( \text{vi} \right) \qquad &a+c=b+c\Rightarrow a=b\qquad &&\text{Cancellation Property w}\text{.r}\text{.t}\text{. addition } \\
  \left( \text{vii} \right) \qquad &5+\left( -5 \right)=0\qquad &&\text{Additive Inverse } \\
 \left( \text{viii} \right) \qquad &7\times \frac{1}{7}=1\qquad &&\text{Multiplicative Inverse } \\
  \left( \text{ix} \right) \qquad &a>b\Rightarrow ac>bc\left( c>0 \right) \qquad &&\text{Multiplicative Property } \\
\end{align}\]

\[\begin{align}
  & 3x+3\left( y-x \right) \\
 & =3x+3y-3x…\qquad&&\text{ Distributive Property} \\
 & =3x-3x+3y… \qquad&&\text{ Commutative Property} \\
 & =0+3y… \qquad&&\text{ Additive Inverse} \\
 & =3y… \qquad&&\text{ Additive Identity} \\
\end{align}\]

\[\begin{align}
  \left( \text{i} \right)\qquad&\sqrt{24}+0=\sqrt{24}\qquad&&\text{Additive Identity} \\
  \left( \text{ii} \right) \qquad&-\frac{2}{3}\left( 5+\frac{7}{2} \right)\text{=}\left( -\frac{2}{3} \right)\left(5\right)\text{+}\left( -\frac{2}{3} \right)\left( \frac{7}{2} \right) \qquad&&\text{Distributive Property} \\
  \left( \text{iii} \right) \qquad&\pi \text{+}\left( -\pi  \right)=0\qquad&&\text{Additive Inverse} \\
  \left( \text{iv} \right) \qquad&\sqrt{3}.\sqrt{3}\qquad&&\text{Colsure Property w}\text{.r}\text{.t.}\\
&&&\text{multiplication} \\
  \left( \text{v} \right) \qquad&\left( -\frac{5}{8} \right)\left( -\frac{5}{8} \right)=1\qquad&&\text{Multiplicative Inverse} \\
\end{align}\]