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Question
Verify the property x × (y + z) = x × y + x × z of rational numbers by taking.
`x = (-1)/2, y = 2/3, z = 3/4`
Solution
Given, `x = (-1)/2, y = 2/3, z = 3/4`
Now, LHS = x × (y + z)
= `(-1)/2 xx (2/3 + 3/4)`
= `(-1)/2 xx ((8 + 9)/12)`
= `(-1)/2 xx 17/12`
= `(-17)/24`
And RHS = x × y + x × z
= `(-1)/2 xx 2/3 + ((-1)/2) xx 3/4`
= `(-1)/3 - 3/8`
= `(-8 - 9)/24`
= `(-17)/24`
∴ LHS = RHS
Hence, x × (y + z) = x × y + x × z
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