Question

Determine o valor de x em cada uma das proporções a seguir.
9/63=x/7
2,5/x= 5/10
2/9=x+8/x+50
X/56 =11,2/4
Atividade livro aprender sempre pg 60

Answer 1

Uma proporção é uma igualdade entre razões.

Para determinar o valor de x nas proporções, podemos fazer manipulações algébricas, veja:

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Item 1)

$\begin{array}{l}\sf\dfrac{9}{63}=\dfrac{x}{7}\\\\\sf7\cdot\dfrac{9}{63}=\dfrac{x}{7}\cdot7\\\\\sf\dfrac{63}{63}=x\\\\\!\boxed{\sf x=1}\end{array}$

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Item 2)

$\begin{array}{l}\sf\dfrac{2,5}{x}=\dfrac{5}{10}\\\\\sf10\cdot\dfrac{2,5}{x}=\dfrac{5}{10}\cdot10\\\\\sf\dfrac{25}{x}=5\\\\\sf x\cdot\dfrac{25}{x}=5\cdot x\\\\\sf25=5x\\\\\sf\dfrac{25}{5}=\dfrac{5x}{5}\\\\\!\boxed{\sf x=5}\end{array}$

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Item 3)

$\begin{array}{l}\sf\dfrac{2}{9}=\dfrac{x+8}{x+50}\\\\\sf(x+50)\cdot\dfrac{2}{9}=\dfrac{x+8}{x+50}\cdot(x+50)\\\\\sf\dfrac{2x+100}{9}=x+8\\\\\sf9\cdot\dfrac{2x+100}{9}=(x+8)\cdot9\\\\\sf2x+100=9x+72\\\\\sf9x+72=2x+100\\\\\sf-2x+9x+72=2x+100-2x\\\\\sf7x+72=100\\\\\sf-72+7x+72=100-72\\\\\sf7x=28\\\\\sf\dfrac{7x}{7}=\dfrac{28}{7}\\\\\!\boxed{\sf x=4}\end{array}$

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Item 4)

$\begin{array}{l}\sf\dfrac{x}{56}=\dfrac{11,2}{4}\\\\\sf56\cdot\dfrac{x}{56}=\dfrac{11,2}{4}\cdot56\\\\\sf x=\dfrac{627,2}{4}\\\\\!\boxed{\sf x=156,8}\end{array}$

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Att. Nasgovaskov

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