Question

Resolva as as equações de 1º grau
a)5x= 8x + 3
b)5(x+ 2)= 2(3 +x)
c)3x/2 = 6
d)x5+8=10
e)5X-2=3(X+4)
f)3x+6=4x+2 ​

Answer 1

Calculando, iremos obter:

$\boxed{\boxed{\begin{array}{lr}\boldsymbol{a) - 1}\end{array}}}\boxed{\boxed{\begin{array}{lr}\boldsymbol{b) - 1.3}\end{array}}}\boxed{\boxed{\begin{array}{lr}\boldsymbol{c)4}\end{array}}} \\ \boxed{\boxed{\begin{array}{lr}\boldsymbol{d) \: 0.4}\end{array}}}\boxed{\boxed{\begin{array}{lr}\boldsymbol{e) \: 7}\end{array}}} \\ \boxed{\boxed{\begin{array}{lr}\boldsymbol{f) \: 4}\end{array}}}$

$\overline{\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \:\:\: \: \: \: \: \: \: \: \: \: \begin{Vmatrix}< \heartsuit >\end{Vmatrix} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:}}$

Para obtermos os resultados das equações do 1° Grau, temos de mover a variável, somar os opostos... colocar os termos similares em evidência, logo, somar/subtrair os coeficientes, e por fim, dividir.

Resolva as as equações de 1º grau.

• A) 5x= 8x + 3:

$\boxed{\boxed{\begin{array}{lr}\boldsymbol{5x = 8x + 3} \\\boldsymbol{5x - 8x = 3} \\ \boldsymbol{ \: \: \: - 3x = 3} \\ \boldsymbol{ \: \: \: \: \: x = - 1}\end{array}}}$

• B) 5(x+ 2)= 2(3 +x):

$\boxed{\boxed{\begin{array}{lr}\boldsymbol{5(x + 2) = 2(3 + x)} \\ \boldsymbol{5x + 10 = 2(3 + x)} \\ \boldsymbol{5x + 10 = 6 + 2x} \\ \boldsymbol{5x + 10 - 2x = 6} \\ \boldsymbol{5x - 2x = 6 - 10} \\ \boldsymbol{3x = 6 - 10} \\\boldsymbol{3x = - 4} \\\boldsymbol{x = - 1.3} \end{array}}}$

• C) 3x/2 = 6:

$\boxed{\boxed{\begin{array}{lr}\boldsymbol{ \: \: \: \: \: \: \: \: \frac{3x}{2} = 6} \\ \\ \boldsymbol{ \frac{2}{3} \times \frac{3x}{2} = \frac{2}{3} \times 6 } \\ \\\boldsymbol{ \frac{1}{3} \times 3x = \frac{2}{3} \times 6 } \\ \\\boldsymbol{ \: \: \: \: \: x = \frac{2}{3} \times 6} \\ \\\boldsymbol{ \: \: \: \: \: x = 2 \times 2} \\ \\\boldsymbol{ \: \: \: \: \: \: \: \: \: x = 4} \end{array}}}$

• D) x5+8=10:

$\boxed{\boxed{\begin{array}{lr}\boldsymbol{x5 + 8 = 10} \\\boldsymbol{5x + 8 = 10} \\\boldsymbol{5x = 10 - 8} \\\boldsymbol{5x = 2} \\\boldsymbol{x = 0.4} \end{array}}}$

• E) 5x-2=3(x+4):

$\boxed{\boxed{\begin{array}{lr}\boldsymbol{5x - 2 = 3(x + 4)} \\ \boldsymbol{5x - 2 = 3x + 12} \\ \boldsymbol{5x - 2 - 3x = 12} \\ \boldsymbol{5x - 3x = 12 + 2} \\ \boldsymbol{2x = 12 + 2} \\\boldsymbol{2x = 14} \\\boldsymbol{x = 7} \end{array}}}$

• F) 3x+6=4x+2:

$\boxed{\boxed{\begin{array}{lr}\boldsymbol{3x + 6 = 4x + 2} \\ \boldsymbol{3x + 6 - 4x = 2} \\ \boldsymbol{3x - 4x = 2 - 6} \\ \boldsymbol{ - x = 2 - 6} \\\boldsymbol{ - x = - 4} \\ \boldsymbol{x = 4} \end{array}}}$

$\green{\begin{array}{lr} ............................................................ \end{array}}$

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$\green{\begin{array}{lr} ............................................................ \end{array}}$

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