Question

By taking x= -5/3 ,y= 2/7 and z= 1/-4 , verify that --
(i) x ÷ (y + z) is not equal to x ÷ y + x ÷ Z
(ii) x ÷ (x - z) is not equal to x÷ y - X ÷ Z
(iii) (x + y) ÷ z = x ÷ z + y ÷ Z​

Answer 1

Step-by-step explanation:

Answer

Open in answr app

x=94,y=12−7,z=3−2 then 

x−(y−2)=(x−y)−z

⇒94−[12−7−(3−2)]=[94−(12−7)]−(3−2)

⇒94−[12−7+32]=[94+127]−(3−2)

⇒94−[1

Answer 2

$\bf \underline{ \underline{\maltese\:Given} }$

$\sf \implies x = \dfrac{ - 5}{3} \: \: , \: \: y= \dfrac{2}{7} \: \: , \: \:and \: \: z = \dfrac{1}{ - 4}$

$\bf \underline{ \underline{\maltese \: To \: verify} }$

$\sf (i) \: x \div (y + z) \not= x \div y + x \div z$

$\sf (ii) \: x \div (x - z) \not= x \div y - x \div z$

$\sf (iii) \: (x + y) \div z = x \div z + y \div z$

$\bf \underline{ \underline{\maltese \: Solution} }$

$\sf (i) \: x \div (y + z) \not= x \div y + x \div Z$

$\sf \implies \dfrac{ - 5}{3} \div \bigg(\dfrac{2}{7} +\dfrac{1}{ - 4} \bigg) \not= \dfrac{ - 5}{3} \div \dfrac{2}{7} + \dfrac{ - 5}{3} \div \dfrac{1}{ - 4}$

$\sf \implies \dfrac{ - 5}{3} \div \bigg(\dfrac{8 + ( - 7)}{28} \bigg) \not= \dfrac{ - 5}{3} \times \dfrac{7}{2} + \dfrac{ - 5}{3} \times \dfrac{ - 4}{1}$

$\sf \implies \dfrac{ - 5}{3} \div \dfrac{1}{28} \not= \dfrac{ - 35}{6} + \dfrac{20}{3}$

$\sf \implies \dfrac{ - 5}{3} \times \dfrac{28}{1} \not= \dfrac{ - 35}{6} + \dfrac{20}{3}$

$\sf \implies \dfrac{ - 5}{ 3} \times \dfrac{ 28}{1} \not= \dfrac{ - 35 + 40}{6}$

$\sf \implies \dfrac{ - 140}{ 3} \not= \dfrac{ 5}{6}$

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$\sf (ii) \: x \div (x - z) \not= x \div y - x \div z$

$\sf \implies \dfrac{ - 5}{3} \div \bigg(\dfrac{ - 5}{3} - \dfrac{1}{ - 4} \bigg) \not= \dfrac{ - 5}{3} \div \dfrac{2}{7} - \dfrac{ - 5}{3} \div \dfrac{1}{ - 4}$

$\sf \implies \dfrac{ - 5}{3} \div \bigg(\dfrac{ - 5}{3} + \dfrac{1}{ 4} \bigg) \not= \dfrac{ - 5}{3} \times \dfrac{7}{2} - \dfrac{ - 5}{3} \times \dfrac{ - 4}{ 1}$

$\sf \implies \dfrac{ - 5}{3} \div \bigg(\dfrac{ - 20 + 3}{12} \bigg) \not= \dfrac{ - 35}{6} - \dfrac{ 20}{3}$

$\sf \implies \dfrac{ - 5}{3} \div \dfrac{ - 17}{12} \not= \dfrac{ - 35}{6} - \dfrac{20}{3}$

$\sf \implies \dfrac{ - 5}{3} \times \dfrac{ - 12}{17} \not= \dfrac{ - 35 - 40}{6}$

$\sf \implies \dfrac{ 20}{17} \not= \cancel\dfrac{ - 75}{6}$

$\sf \implies \dfrac{ 20}{17} \not=\dfrac{ - 25}{3}$

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$\sf (iii) \: (x + y) \div z = x \div z + y \div z$

$\sf \implies \bigg(\dfrac{ - 5}{3} + \dfrac{2}{7}\bigg) \div \dfrac{1}{ - 4} = \dfrac{ - 5}{3} \div \dfrac{1}{ - 4} + \dfrac{2}{7} \div \dfrac{1}{ - 4}$

$\sf \implies \bigg(\dfrac{ - 35 + 6}{21} \bigg) \div \dfrac{1}{ - 4} = \dfrac{ - 5}{3} \times \dfrac{ - 4}{1} + \dfrac{2}{7} \times \dfrac{ - 4}{1}$

$\sf \implies \dfrac{ - 29}{21} \div \dfrac{1}{ - 4} = \dfrac{ 20}{3} + \dfrac{-8}{7}$

$\sf \implies \dfrac{ - 29}{21} \times \dfrac{-4}{1} = \dfrac{ 20}{3} -\dfrac{8}{7}$

$\sf \implies \dfrac{116}{21} = \dfrac{ 140-24}{21}$

$\sf \implies \dfrac{116}{21} = \dfrac{ 116}{21}$

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