Question

the rational x is such that when we multipy it by 3/4 and add 5 then it becomes 1/2 find the number

Answer 1

Answer :-

• The required number is -6.

To find :-

• The number.

Step-by-step explanation :-

• Here, it has been given that when the rational number x is multiplied by 3/4 and 5 is added, it becomes 1/2. We have to find the number.

Calculations :-

$\rm Multiplying \: x \: with \: \dfrac{3}{4} , we \: get \: x \times \dfrac{3}{4}$

$\rm Adding \: 5 \: to \: it, we \: get \: x \times \dfrac{3}{4} + 5$

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Now, it has been given that :-

• The result is 1/2.

Therefore,

$\sf x \times \dfrac{3}{4} + 5 = \dfrac{1}{2}$

Multiplying 3/4 with x,

$\sf \dfrac{3x}{4} + 5 = \dfrac{1}{2}$

Transposing 5 from LHS to RHS, changing it's sign,

$\sf\dfrac{3x}{4} = \dfrac{1}{2} - 5$

The LCM of 2 and 1 is 2, so subtracting the fractions using their denominators,

$\sf\dfrac{3x}{4} = \dfrac{1 \times 1 - 5 \times 2}{2}$

On simplifying,

$\sf\dfrac{3x}{4} = \dfrac{1 - 10}{2}$

Subtracting 10 from 1,

$\sf\dfrac{3x}{4} = \dfrac{ - 9}{ \: \: \: 2}$

Transposing 4 from LHS to RHS, changing it's sign,

$\sf3x = \dfrac{ - 9}{ \: \: \: \cancel{2}} \times \cancel{4}$

Reducing the numbers,

$\sf 3x = \dfrac{ - 9}{ \: \: \: 1} \times 2$

Multiplying 9 with 2,

$\sf3x = \dfrac{ - 18}{ \: \: \: \: \: 1}$

Removing the denominator of the fraction,

$\sf3x = - 18$

Transposing 3 from LHS to RHS, changing it's sign,

$\sf x = \dfrac{ - 18}{ \: \: \: \: \: 3}$

Dividing -18 by 3,

$\underline{ \boxed{\sf x = - 6}}$

• Hence, the value of the rational number x is -6.

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