Question

Resolva as equações :
A)x/5=9/15
B)4/x=6/9
C)1/3=x/42
D)x-1/10=x-9/2
E)x-1/3=2x+1/3
F)x/5-x/6=1/4
G)2x/3-3x/2=5
H)7x/2+3/5=4x

Answer 1

Olá.

 

Usaremos propriedades básicas de equações de primeiro grau. Uma das coisas que serão feitas nos desenvolvimentos é: “igualar denominadores”, que será feito a partir do produto dos denominadores e as diferenças sendo multiplicadas nos denominadores. 

Vamos aos cálculos de cada caso

 

A)

$\mathsf{\dfrac{x}{5}=\dfrac{9}{15}}\\\\\mathsf{9\cdot5=15\cdot x}\\\\\mathsf{45=15\cdot x}\\\\\mathsf{\dfrac{45}{15}=x}\\\\\boxed{\mathsf{3=x}}$

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B)

$\mathsf{\dfrac{4}{x}=\dfrac{6}{9}}\\\\\mathsf{x\cdot6=4\cdot9}\\\\\mathsf{x\cdot6=36}\\\\\mathsf{x=\dfrac{36}{6}}\\\\\boxed{\mathsf{x=6}}$

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C)

$\mathsf{\dfrac{1}{3}=\dfrac{x}{42}}\\\\\mathsf{1\cdot42=3\cdot x}\\\\\mathsf{42=3\cdot x}\\\\\mathsf{\dfrac{42}{3}=x}\\\\\boxed{\mathsf{14=x}}$

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D)

$\mathsf{\dfrac{x-1}{10}=\dfrac{x-9}{2}}\\\\\mathsf{(x-1)\cdot2=(x-9)\cdot10}\\\\\mathsf{2x-2=10x-90}\\\\\mathsf{2x-10x=-90+2}\\\\\mathsf{-8x=-88}\\\\\mathsf{x=\dfrac{-88}{-8}}\\\\\boxed{\mathsf{x=11}}$

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E)

$\mathsf{\dfrac{x-1}{3}=\dfrac{2x+1}{3}}\\\\\mathsf{(x-1)\cdot3=(2x+1)\cdot3}\\\\\mathsf{3x-3=6x+3}\\\\\mathsf{3x-6x=3+3}\\\\\mathsf{-3x=6}\\\\\mathsf{x=\dfrac{6}{-3}}\\\\\boxed{\mathsf{x=-2}}$

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F)

$\mathsf{\dfrac{x}{5}-\dfrac{x}{6}=\dfrac{1}{4}}\\\\\\\mathsf{\dfrac{6x-5x}{30}=\dfrac{1}{4}}\\\\\\\mathsf{\dfrac{x}{30}=\dfrac{1}{4}}\\\\\mathsf{x\cdot4=30\cdot1}\\\\\mathsf{4x=30}\\\\\mathsf{x=\dfrac{30}{4}}\\\\\boxed{\mathsf{x=7,5}}$

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G)

$\mathsf{\dfrac{2x}{3}-\dfrac{3x}{2}=5}\\\\\\\mathsf{\dfrac{4x-9x}{6}=5}\\\\\\\mathsf{\dfrac{-5x}{6}=5}\\\\\mathsf{-5x=5\cdot6}\\\\\mathsf{-5x=30}\\\\\mathsf{x=\dfrac{30}{-5}}\\\\\boxed{\mathsf{x=-6}}$

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H)

$\mathsf{\dfrac{7x}{2}+\dfrac{3}{5}=4x}\\\\\\\mathsf{\dfrac{35x+6}{10}=4x}\\\\\mathsf{35x+6=4x\cdot10}\\\\\mathsf{35x+6=40x}\\\\\mathsf{6=40x-35x}\\\\\mathsf{6=5x}\\\\\mathsf{\dfrac{6}{5}=x}\\\\\boxed{\mathsf{1,2=x}}$

 

Qualquer dúvida, deixe nos comentários.

Bons estudos$.$