Question

1-Resolva as equações a seguir
A) x-5/10 + 1-2x/5 = 3-x/4
B) 9x-75/x = 34
C) 5(m-2)/2 - 2(m+4)/3 = 3(m-1)/2

Answer 1

Resposta:

Solução:

$\sf \displaystyle \dfrac{x - 5 }{10} + \dfrac{1 -2x}{5} = \dfrac{3 -x}{4} \quad \gets \text{\sf m.m.c de \{ 10, 5, 4 \} = 20}}$

$\sf \displaystyle \dfrac{2\cdot (x - 5 )}{20} + \dfrac{4 \cdot (1 -2x)}{20} = \dfrac{5 \cdot (3 -x)}{20} \quad \gets \text{\sf Cancelar o denominador.}}$

$\sf \displaystyle 2 \cdot (x - 5) + 4 \cdot (1- 2x) = 5 \cdot (3-x)$

$\sf \displaystyle 2x - 10 + 4 -8x = 15 -5x$

$\sf \displaystyle 2x - 8x + 5x = 15 + 10 - 4$

$\sf \displaystyle - x = 21$

$\boxed{ \boxed { \boldsymbol{ \sf \displaystyle x = - \: 21 }}} \quad \gets \mathbf{ Resposta }$

B)

$\sf \displaystyle \dfrac{9x - 75}{x} = 34$

$\sf \displaystyle 34x = 9x - 75$

$\sf \displaystyle 34x -9x = 75$

$\sf \displaystyle 25 x = 75$

$\sf \displaystyle x = \dfrac{75}{25}$

$\boxed{ \boxed { \boldsymbol{ \sf \displaystyle x = 3 }}} \quad \gets \mathbf{ Resposta }$

C)

$\sf \displaystyle \dfrac{5 \cdot (m- 2)}{2} - \dfrac{2 \cdot (m +4)}{3} = \dfrac{3 \cdot (m- 1)}{2}$

$\sf \displaystyle \dfrac{15 \cdot (m- 2)}{6} - \dfrac{4 \cdot (m +4)}{6} = \dfrac{9\cdot (m- 1)}{6}$

$\sf \displaystyle 15 \cdot (m - 2) - 4 \cdot (m +4) = 9 \cdot ( m-1)$

$\sf \displaystyle 15 m- 30 -4m - 16 = 9m - 9$

$\sf \displaystyle 15m - 4m - 9m = 30 + 16 - 9$

$\sf \displaystyle 15m - 13 m = 46 -9$

$\sf \displaystyle 2m = 37$

$\sf \displaystyle m = \dfrac{37}{2}$

$\boxed{ \boxed { \boldsymbol{ \sf \displaystyle m =18,5 }}} \quad \gets \mathbf{ Resposta }$

Explicação passo-a-passo: