Verify the property $ x \times(y+z)=(x \times y)+(x \times z) $ for the given values of $ x,\ y $ and $ z $.$ x=\frac{-5}{2}, y=\frac{1}{2} $ and $ z=-\frac{10}{7} $>

Given:  $x=\frac{-5}{2},\ y=\frac{1}{2}$ and $z=-\frac{10}{7}$. 

To do: To verify the property $x\times(y+z)=( x\times y)+( x\times z)$ for the given values of  $x,\ y$ and $z$.
 

Solution:

$L.H.S.=x\times( y+z)$

$=\frac{-5}{2}\times( \frac{1}{2}-\frac{10}{7})$                 [On substituting values of $x,\ y$ and $z$]

$=-\frac{5}{2}\times\frac{-13}{14}$

$=\frac{65}{28}$

$R.H.S.=( x\times y)+( x\times z)$

$=( \frac{-5}{2}\times\frac{1}{2})+( \frac{-5}{2}\times-\frac{10}{7})$

$=-\frac{5}{4}+\frac{50}{14}$

$=-\frac{5}{4}\times\frac{7}{7}+\frac{50}{14}$

$=-\frac{35}{28}+\frac{100}{28}$

$=\frac{65}{28}$

Thus $L.H.S.=R.H.S.$

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Updated on: 10-Oct-2022

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