Question

the sum of two rational numbers is -4 if one of them is -11/5 find the other​

Answer 1

Step-by-step explanation:

the sum of two rational numbers is -4 if one of them is -11/5 find the other

Answer 2

Given :

• Sum of two rational numbers is ( -4 )

• One of the number is $\bf\:\frac{-11}{5}$

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To find :

• The other number sum of which with $\bf\:\frac{-11}{5}$ gives ( -4 )

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Concept :

In this question we are said that the sum of two rational numbers is ( -4 ) . One of the number is given as $\bf\:\frac{-11}{5}$ . We are asked to find the other rational number . So for this we would assume any variable as the other number . Then after we would form an equation following the criteria of the question . Solving the equation we would get our final answer.

Hope am clear let's solve it :D~

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Assumption :

Let the other rational number be x.

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Solution :

According to the question -

Sum of x and $\tt\:\frac{-11}{5}$ = ( -4 )

$\tt\implies\:x+(\frac{-11}{5})=(-4)$

Multiplying the signs

$\tt\implies\:x-\frac{11}{5}=(-4)$

LCM of 1 and 5 = 5

$\tt\implies\:\frac{(5 \times x) - ( 1 \times 11)}{5}=(-4)$

$\tt\implies\:\frac{5x - 11}{5}=(-4)$

Cross multiplying

$\tt\implies\:5x - 11=(-4) \times 5$

$\tt\implies\:5x - 11=(-20)$

Transposing (-11) to RHS it becomes +11

$\tt\implies\:5x =(-20)+11$

$\tt\implies\:5x =(-9)$

Transposing 5 to RHS it goes to the denominator

$\small{\underline{\boxed{\mathrm{\implies\:x=(\frac{-9}{5})}}}}$ ★

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Verifying :

Plugging the value of x as -9/5 in the equation formed earlier -

$\tt\:x+(\frac{-11}{5})=(-4)$

$\tt\mapsto\:\frac{-9}{5}+(\frac{-11}{5})=(-4)$

$\tt\mapsto\:\frac{-9}{5}-\frac{11}{5}=(-4)$

LCM of 5 and 5 = 5

$\tt\mapsto\:\frac{-9}{5}-\frac{11}{5}=(-4)$

$\tt\mapsto\:\frac{-9-11}{5}=(-4)$

$\tt\mapsto\:\frac{-20}{5}=(-4)$

Cross multiplying

$\tt\mapsto\:-20=(-4) \times 5$

$\tt\mapsto\:-20=-20$

$\bf\mapsto\:LHS=RHS$

Hence Verified !~

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Therefore :

⠀⠀ ⠀⠀ ⠀❒ The other rational number is $\large{\mathfrak\red{(\frac{-9}{5})}}$

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