Question

d) 5x - 2.(3x+4)= 25 - 3.(5x+1)​

Answer 1

Tarea:

$5x - 2(3x+4)= 25 - 3(5x+1)$

Solución:

$5x - 2(3x+4)= 25 - 3(5x+1)$

→ desarrollar paréntesis: $a(b + c) = ab + ac$

$-----------------$

primer miembro:

$= 5x - 2(3x+4)$

$= 5x - 2\cdot3x+(-2)\cdot4$

$= 5x - 6x-2\cdot4$

$= 5x - 6x-8$                      

$\boxed{= -x-8}$    

segundo miembro:

$= 25 - 3(5x+1)$

$= 25 - 3\cdot5x+(-3)\cdot1$

$= 25 - 15x+(-3)\cdot1$

$= 25 - 15x-3\cdot1$

$= 25 - 15x-3$

$= 25 -3 -15x$

$\boxed{= 22-15x}$

$-----------------$

$-x-8=22-15x$

→ sumo 8 ambos lados:

$-x-8+8=22-15x + 8$

→ simplificar:

$-x = 30 -15x$

→ sumo 15x ambos lados:

$-x + 15x= 30 -15x + 15x$

→ simplificar:

$14x = 30$

→ dividir ambos lados entre 14:

$\dfrac{14x}{14} = \dfrac{30}{14}$

→ simplificar:

$x = \dfrac{30}{14}$

$\boxed{x=\dfrac{15}{7}}$ ⇒⇒⇒⇒ Respuesta

Comprobamos:

$5x - 2(3x+4)= 25 - 3(5x+1)$

$5\left(\dfrac{15}{7}\right) - 2\left(3\left(\dfrac{15}{7}\right)+4\right)= 25 - 3\left(5\left(\dfrac{15}{7}\right)+1\right)$

$5\cdot\dfrac{15}{7} - 2\left(3\cdot\dfrac{15}{7}+4\right)= 25 - 3\left(5\cdot\dfrac{15}{7}+1\right)$

$5\cdot\dfrac{15}{7} - 2\left(\dfrac{3}{1} \cdot\dfrac{15}{7}+\dfrac{4\cdot7}{7} \right)= 25 - 3\left(\dfrac{5}{1} \cdot\dfrac{15}{7}+\dfrac{7\cdot1}{7} \right)$

$5\cdot\dfrac{15}{7} - 2\left(\dfrac{3\cdot15}{1\cdot7} +\dfrac{4\cdot7}{7} \right)= 25 - 3\left(\dfrac{5\cdot15}{1\cdot7} +\dfrac{7\cdot1}{7} \right)$

$5\cdot\dfrac{15}{7} - 2\left(\dfrac{45}{7} +\dfrac{4\cdot7}{7} \right)= 25 - 3\left(\dfrac{75}{7} +\dfrac{7\cdot1}{7} \right)$

$5\cdot\dfrac{15}{7} - 2\left(\dfrac{45+4\cdot7}{7} \right)= 25 - 3\left(\dfrac{75+7\cdot1}{7} \right)$

$5\cdot\dfrac{15}{7} - 2\left(\dfrac{73}{7} \right)= 25 - 3\left(\dfrac{82}{7} \right)$

$5\cdot\dfrac{15}{7} - 2\cdot\dfrac{73}{7}= 25 - 3\cdot\dfrac{82}{7}$

$\dfrac{5}{1} \cdot\dfrac{15}{7} - \dfrac{2}{1} \cdot\dfrac{73}{7}= 25 -\dfrac{3}{1} \cdot\dfrac{82}{7}$

$\dfrac{5\cdot15}{1\cdot7} - \dfrac{2\cdot73}{1\cdot7}= 25 -\dfrac{3\cdot82}{1\cdot7}$

$\dfrac{75}{7} - \dfrac{146}{7}= 25 -\dfrac{246}{7}$

$\dfrac{75-146}{7} = \dfrac{25\cdot7}{7} -\dfrac{246}{7}$

$-\dfrac{71}{7} = \dfrac{25\cdot7-246}{7}$

$-\dfrac{71}{7} = \dfrac{175-246}{7}$

$\boxed{-\dfrac{71}{7} =- \dfrac{71}{7}}$