Explicação passo-a-passo:
Uma proporção é uma igualdade entre razões.
Para determinar o valor de x nas proporções, podemos fazer manipulações algébricas, veja:
~~
63
9
=
7
x
7⋅
63
9
=
7
x
⋅7
63
63
=x
x=1
~~
Item 2)
\begin{gathered}\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}\end{gathered}
x
2,5
=
10
5
10⋅
x
2,5
=
10
5
⋅10
x
25
=5
x⋅
x
25
=5⋅x
25=5x
5
25
=
5
5x
x=5
~~
Item 3)
\begin{gathered}\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}\end{gathered}
9
2
=
x+50
x+8
(x+50)⋅
9
2
=
x+50
x+8
⋅(x+50)
9
2x+100
=x+8
9⋅
9
2x+100
=(x+8)⋅9
2x+100=9x+72
9x+72=2x+100
−2x+9x+72=2x+100−2x
7x+72=100
−72+7x+72=100−72
7x=28
7
7x
=
7
28
x=4
~~
Item 4)
\begin{gathered}\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}\end{gathered}
56
x
=
4
11,2
56⋅
56
x
=
4
11,2
⋅56
x=
4
627,2
x=156,8
