PENSAMIENTO MATEMAATICO, II UNIDAD II. ECUACIONES DE PRIMER GRADO INO:ACOSTA 2.1 SOLUCIÓN DE ECUACIONES DE PRIMER GRADO INSTRUCCIONES: Resolver las siguiontes ecuaciones. (1) $$ (x+4)^{3}-(x+7)(13 x-1)=(x+6)^{2}+\left(x^{2}+4\right)(x-2) $$ SOLUCIONA ECUACIONES DE PRIMER GRADO (1) $$ x=\frac{63}{x 4} $$ (2) $$ x=\frac{45}{11} $$ (3) $$ x=\frac{15}{25} $$ (4) $$ x=-\frac{13}{4} $$ (5) $$ w=\frac{5}{\pi} $$ (6) $$ x=\frac{1}{3} $$ (7) $$ y=\frac{174}{229} $$ (8) $$ x=-\frac{7}{10} $$ (9) $$ x=-\frac{5}{12} $$ $$ (x-7)^{2}-(x+5)\left(x^{2}-3\right)=(5-2 x)(8 x+8)-(x-4)^{3} $$

Question

UpStudy AI · Accepted Answer

Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$x=\frac{63}{4}$$
Solve the equation $$ x=-\frac{13}{4} $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$x=-\frac{13}{4}$$
Solve the equation $$ y=\frac{174}{229} $$.
Solve the equation by following steps:
- step0: Solve for $$y$$:
  $$y=\frac{174}{229}$$
Solve the equation $$ w=\frac{5}{\pi} $$.
Solve the equation by following steps:
- step0: Solve for $$w$$:
  $$w=\frac{5}{\pi }$$
Solve the equation $$ x=\frac{1}{3} $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$x=\frac{1}{3}$$
Solve the equation $$ x=\frac{45}{11} $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$x=\frac{45}{11}$$
Solve the equation $$ x=-\frac{7}{10} $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$x=-\frac{7}{10}$$
Solve the equation $$ x=-\frac{5}{12} $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$x=-\frac{5}{12}$$
Solve the equation $$ x=\frac{15}{25} $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$x=\frac{15}{25}$$
- step1: Reduce the fraction:
  $$x=\frac{3}{5}$$
Solve the equation $$ (x+4)^{3}-(x+7)(13 x-1)-(x+6)^{2}-(x^{2}+4)(x-2)=0 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\left(x+4\right)^{3}-\left(x+7\right)\left(13x-1\right)-\left(x+6\right)^{2}-\left(x^{2}+4\right)\left(x-2\right)=0$$
- step1: Simplify:
  $$\left(x+4\right)^{3}+\left(-x-7\right)\left(13x-1\right)-\left(x+6\right)^{2}+\left(-x^{2}-4\right)\left(x-2\right)=0$$
- step2: Calculate:
  $$-58x+43=0$$
- step3: Move the constant to the right side:
  $$-58x=0-43$$
- step4: Remove 0:
  $$-58x=-43$$
- step5: Change the signs:
  $$58x=43$$
- step6: Divide both sides:
  $$\frac{58x}{58}=\frac{43}{58}$$
- step7: Divide the numbers:
  $$x=\frac{43}{58}$$
Solve the equation $$ (x-7)^{2}-(x+5)(x^{2}-3)=(5-2 x)(8 x+8)-(x-4)^{3} $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\left(x-7\right)^{2}-\left(x+5\right)\left(x^{2}-3\right)=\left(5-2x\right)\left(8x+8\right)-\left(x-4\right)^{3}$$
- step1: Multiply the terms:
  $$\left(x-7\right)^{2}+\left(-x-5\right)\left(x^{2}-3\right)=\left(5-2x\right)\left(8x+8\right)-\left(x-4\right)^{3}$$
- step2: Move the expression to the left side:
  $$\left(x-7\right)^{2}+\left(-x-5\right)\left(x^{2}-3\right)-\left(\left(5-2x\right)\left(8x+8\right)-\left(x-4\right)^{3}\right)=0$$
- step3: Remove the parentheses:
  $$\left(x-7\right)^{2}+\left(-x-5\right)\left(x^{2}-3\right)+\left(-5+2x\right)\left(8x+8\right)+\left(x-4\right)^{3}=0$$
- step4: Calculate:
  $$13x-40=0$$
- step5: Move the constant to the right side:
  $$13x=0+40$$
- step6: Remove 0:
  $$13x=40$$
- step7: Divide both sides:
  $$\frac{13x}{13}=\frac{40}{13}$$
- step8: Divide the numbers:
  $$x=\frac{40}{13}$$
Vamos a resolver las ecuaciones paso a paso.

### 1. Resolución de la primera ecuación:
$$
(x+4)^{3}-(x+7)(13 x-1)=(x+6)^{2}+(x^{2}+4)(x-2)
$$

Primero, reorganizamos la ecuación para igualarla a cero:
$$
(x+4)^{3}-(x+7)(13 x-1)-(x+6)^{2}-(x^{2}+4)(x-2)=0
$$

Ahora, resolvemos esta ecuación. El resultado es:
$$
x=\frac{43}{58}
$$

### 2. Resolución de la segunda ecuación:
$$
(x-7)^{2}-(x+5)(x^{2}-3)=(5-2 x)(8 x+8)-(x-4)^{3}
$$

Reorganizamos la ecuación para igualarla a cero:
$$
(x-7)^{2}-(x+5)(x^{2}-3)-(5-2 x)(8 x+8)+(x-4)^{3}=0
$$

Resolviendo esta ecuación, obtenemos:
$$
x=\frac{40}{13}
$$

### Resumen de las soluciones:
1. Para la primera ecuación: 
   $$
   x=\frac{43}{58}
   $$
2. Para la segunda ecuación: 
   $$
   x=\frac{40}{13}
   $$

Si necesitas más ayuda o resolver otras ecuaciones, ¡házmelo saber!
Las soluciones de las ecuaciones son: 1. $$ x = \frac{43}{58} $$ 2. $$ x = \frac{40}{13} $$

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Algebra Questions