Question

A rational number is such that when you multiply it by 5/2and add 2/3to the product, you get-7/12. What is the number?

Answer 1

Answer:

-1/2

Step-by-step explanation:

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Answer 2

Given :-

• A rational number is such that when we multiply it by 5/2 and add 2/3 to the product, we will get -7/12.

To Find :-

• What's the number?

Solution :-

• Let the Rational Number be x.It’s given that when we multiply it by 5/2 and add 2/3 to the product, we will get -7/12.

⠀⠀⠀⠀⠀$\small\underline{\pmb{\sf According \: to \: the \: question :-}}$

$\mathsf{\: \: \: \: \: \: \: \:\pink{ :\implies \bigg(\dfrac{5x}{2} + \dfrac{2}{3}\bigg) = -\dfrac{7}{12}}}$

$\mathsf{\: \: \: \: \: \: \: \: :\implies \bigg[\dfrac{3(5x) + 2(2)}{6} \bigg] = -\dfrac{7}{12}}$

$\mathsf{\: \: \: \: \: \: \: \: :\implies \bigg[\dfrac{15x + 4}{6} \bigg] =- \dfrac{7}{12}}$

$\mathsf{\: \: \: \: \: \: \: \: :\implies 12(15x + 4) = - 6\times 7}$

$\mathsf{\: \: \: \: \: \: \: \: :\implies 180x + 48 = - 42}$

$\mathsf{\: \: \: \: \: \: \: \: :\implies 180x = - 42 - 48}$

$\mathsf{\: \: \: \: \: \: \: \: :\implies 180x = -90}$

$\mathsf{\: \: \: \: \: \: \: \: :\implies x= \dfrac{-90}{180}}$

$\mathsf{\: \: \: \: \: \: \: \: :\implies x= \cancel{\dfrac{-90}{180}}}$

$\mathsf{\: \: \: \: \: \: \: \: \pink{:\implies x= \dfrac{-1}{2}}}$

$\therefore\:\underline{\textsf{ The rational number is \textbf{-1/2}}}.$