Chapter 2: Introduction to Linear Polynomials

Exercise

Question

Question: 3

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If we multiply a number by \dfrac{5}{2} and add \dfrac{2}{3} to the product, we get -\dfrac{7}{12}. Find the number.

Answer

1
Let the number be n. Form an equation from the given statement.
$\dfrac{5}{2} × n + \dfrac{2}{3} = -\dfrac{7}{12}$
2
Find the of the denominators 2, 3, and 12 using prime .
Prime factorization of 2 = 2
Prime factorization of 3 = 3
Prime factorization of 12 = $2^2 × 3$
Hence, LCM = $2^2 × 3$ = 12
3
Multiply both sides by 12 to remove the fractions and solve the equation.
\text{$12 × (\dfrac{5}{2}n) + 12 × \dfrac{2}{3} = 12 × (-\dfrac{7}{12})$}
⇒
$30n + 8 = -7$
⇒
$30n = -7 - 8$
⇒
$30n = -15$
⇒
\text{ $n = -\dfrac{15}{30}$}
⇒
\text{ $n = -\dfrac{1}{2}$}
4
Write the number.
\textbf{Answer: -$\dfrac{1}{2}$}
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