(-5)+x=-4/3
x=-4/3+5
x=-4/3+15/3
x=(-4+15)/3
x=11/3
Appropriate Question :
The sum of two rational numbers is - [tex]\frac{4}{3}[/tex]. If one of the number is -5, then find the other number.
Answer:
[tex]\qquad\qquad\boxed{ \sf{ \: \sf \: Other\:rational\:number \: = \: \dfrac{11}{3} \: }} \\ \\ [/tex]
Step-by-step explanation:
[tex]\large\underline{\sf{Given- }}[/tex]
The sum of two rational numbers is - [tex]\frac{4}{3} [/tex].
One of the number is - 5.
[tex] \\ \large\underline{\sf{To\:Find - }}[/tex]
The other number.
[tex] \\ \\ \large\underline{\sf{Solution-}}[/tex]
Given that,
The sum of two rational numbers is - [tex]\frac{4}{3}[/tex].
Let assume other number be x.
According to statement
[tex]\sf \: x + (-5) = - \dfrac{4}{3} \\ \\ [/tex]
[tex]\sf \: x - 5 = - \dfrac{4}{3} \\ \\ [/tex]
[tex]\sf \: x = 5 - \dfrac{4}{3} \\ \\ [/tex]
[tex]\sf \: x = \dfrac{15}{3} - \dfrac{4}{3} \\ \\ [/tex]
[tex]\sf \: x = \dfrac{15 - 4}{3} \\ \\ [/tex]
[tex]\sf \:\bf\implies \: x = \dfrac{11}{3} \\ \\ [/tex]
Hence,
[tex]\sf\implies \sf \: Other\:rational\:number \: = \: \dfrac{11}{3} \\ \\ [/tex]
[tex] \rule{190pt}{2pt}[/tex]
Additional Information
[tex]\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{{More \: identities}}}} \\ \\ \bigstar \: \bf{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \bigstar \: \bf{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \bigstar \: \bf{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \end{array} }}\end{gathered}\end{gathered}\end{gathered} [/tex]
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Answers & Comments
(-5)+x=-4/3
x=-4/3+5
x=-4/3+15/3
x=(-4+15)/3
x=11/3
Verified answer
Appropriate Question :
The sum of two rational numbers is - [tex]\frac{4}{3}[/tex]. If one of the number is -5, then find the other number.
Answer:
[tex]\qquad\qquad\boxed{ \sf{ \: \sf \: Other\:rational\:number \: = \: \dfrac{11}{3} \: }} \\ \\ [/tex]
Step-by-step explanation:
[tex]\large\underline{\sf{Given- }}[/tex]
The sum of two rational numbers is - [tex]\frac{4}{3} [/tex].
One of the number is - 5.
[tex] \\ \large\underline{\sf{To\:Find - }}[/tex]
The other number.
[tex] \\ \\ \large\underline{\sf{Solution-}}[/tex]
Given that,
The sum of two rational numbers is - [tex]\frac{4}{3}[/tex].
One of the number is - 5.
Let assume other number be x.
According to statement
[tex]\sf \: x + (-5) = - \dfrac{4}{3} \\ \\ [/tex]
[tex]\sf \: x - 5 = - \dfrac{4}{3} \\ \\ [/tex]
[tex]\sf \: x = 5 - \dfrac{4}{3} \\ \\ [/tex]
[tex]\sf \: x = \dfrac{15}{3} - \dfrac{4}{3} \\ \\ [/tex]
[tex]\sf \: x = \dfrac{15 - 4}{3} \\ \\ [/tex]
[tex]\sf \:\bf\implies \: x = \dfrac{11}{3} \\ \\ [/tex]
Hence,
[tex]\sf\implies \sf \: Other\:rational\:number \: = \: \dfrac{11}{3} \\ \\ [/tex]
[tex] \rule{190pt}{2pt}[/tex]
Additional Information
[tex]\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{{More \: identities}}}} \\ \\ \bigstar \: \bf{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \bigstar \: \bf{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \bigstar \: \bf{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \end{array} }}\end{gathered}\end{gathered}\end{gathered} [/tex]