Answer: Let the other number be x. x + 5/9 = -23/9 x = -23/9 – 5/9 x = -28/9 Hence the other number is -28/9. Reply
❍ Let’s Consider second rational number be x . Given that , The sum of two rational numbers-23/9.if one of the members is 5/9. Then , [tex]\star\sf{ Equation = \dfrac{5}{9} + x = \dfrac{-23}{9}}\\[/tex] ⠀⠀⠀⠀⠀⠀[tex]\underline {\bf{\star\:Now \: By \: Solving\:for\:x \:in\: the \: Formed \: Equation \::}}\\[/tex] [tex]\qquad:\implies\sf{ Equation = \dfrac{5}{9} + x = \dfrac{-23}{9}}\\[/tex] [tex]\qquad:\implies\sf{ \dfrac{5}{9} + x = \dfrac{-23}{9}}\\[/tex] [tex]\qquad:\implies\sf{ x = \dfrac{-23}{9}-\dfrac{5}{9}}\\[/tex] [tex]\qquad:\implies\sf{ x = \dfrac{-23-5}{9}}\\[/tex] [tex]\qquad:\implies\sf{ x = \dfrac{-28}{9}}\\[/tex] ⠀⠀⠀⠀⠀[tex]\underline {\boxed{\pink{ \mathrm { x = \dfrac{-28}{9}\: }}}}\:\bf{\bigstar}\\[/tex] Therefore, ⠀⠀⠀⠀⠀[tex]\therefore {\underline{ \mathrm { Hence,\:The\:Second \:Rational \:number \:is\:\bf{\dfrac{-28}{9}\: }}}}\\[/tex] ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀ V E R I F I C A T I O N : As, We know that , [tex]\star\sf{ Equation = \dfrac{5}{9} + x = \dfrac{-23}{9}}\\[/tex] Where, [tex]\qquad:\implies\sf{ x = \dfrac{-28}{9}}\\[/tex] ⠀⠀⠀⠀⠀⠀[tex]\underline {\bf{\star\:Now \: By \: Substituting \:\:x \:in\: the \: Formed \: Equation \::}}\\[/tex] [tex]\qquad:\implies\sf{ Equation = \dfrac{5}{9} + \dfrac{-28}{9} = \dfrac{-23}{9}}\\[/tex] [tex]\qquad:\implies\sf{ \dfrac{5}{9} + \dfrac{-28}{9} = \dfrac{-23}{9}}\\[/tex] [tex]\qquad:\implies\sf{ \dfrac{5+ (-28)}{9} = \dfrac{-23}{9}}\\[/tex] [tex]\qquad:\implies\sf{ \dfrac{5 -28}{9} = \dfrac{-23}{9}}\\[/tex] [tex]\qquad:\implies\sf{ \dfrac{-23}{9} = \dfrac{-23}{9}}\\[/tex] ⠀⠀⠀⠀⠀[tex]\therefore {\underline {\bf{ Hence, \:Verified \:}}}\\[/tex] ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀ Reply
Answer:
Let the other number be x.
x + 5/9 = -23/9
x = -23/9 – 5/9
x = -28/9
Hence the other number is -28/9.
❍ Let’s Consider second rational number be x .
Given that ,
Then ,
⠀⠀⠀⠀⠀⠀[tex]\underline {\bf{\star\:Now \: By \: Solving\:for\:x \:in\: the \: Formed \: Equation \::}}\\[/tex]
[tex]\qquad:\implies\sf{ Equation = \dfrac{5}{9} + x = \dfrac{-23}{9}}\\[/tex]
[tex]\qquad:\implies\sf{ \dfrac{5}{9} + x = \dfrac{-23}{9}}\\[/tex]
[tex]\qquad:\implies\sf{ x = \dfrac{-23}{9}-\dfrac{5}{9}}\\[/tex]
[tex]\qquad:\implies\sf{ x = \dfrac{-23-5}{9}}\\[/tex]
[tex]\qquad:\implies\sf{ x = \dfrac{-28}{9}}\\[/tex]
⠀⠀⠀⠀⠀[tex]\underline {\boxed{\pink{ \mathrm { x = \dfrac{-28}{9}\: }}}}\:\bf{\bigstar}\\[/tex]
Therefore,
⠀⠀⠀⠀⠀[tex]\therefore {\underline{ \mathrm { Hence,\:The\:Second \:Rational \:number \:is\:\bf{\dfrac{-28}{9}\: }}}}\\[/tex]
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V E R I F I C A T I O N :
As, We know that ,
Where,
⠀⠀⠀⠀⠀⠀[tex]\underline {\bf{\star\:Now \: By \: Substituting \:\:x \:in\: the \: Formed \: Equation \::}}\\[/tex]
[tex]\qquad:\implies\sf{ Equation = \dfrac{5}{9} + \dfrac{-28}{9} = \dfrac{-23}{9}}\\[/tex]
[tex]\qquad:\implies\sf{ \dfrac{5}{9} + \dfrac{-28}{9} = \dfrac{-23}{9}}\\[/tex]
[tex]\qquad:\implies\sf{ \dfrac{5+ (-28)}{9} = \dfrac{-23}{9}}\\[/tex]
[tex]\qquad:\implies\sf{ \dfrac{5 -28}{9} = \dfrac{-23}{9}}\\[/tex]
[tex]\qquad:\implies\sf{ \dfrac{-23}{9} = \dfrac{-23}{9}}\\[/tex]
⠀⠀⠀⠀⠀[tex]\therefore {\underline {\bf{ Hence, \:Verified \:}}}\\[/tex]
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