Matemáticas 1 · Tema 3
Ecuaciones
Video
Ejemplo
Resuelve las siguientes ecuaciones:
$$\begin{aligned}
3+4(2x-1) &= 1-2(3-5x) \\
3+8x-4 &= 1-6+10x \\
8x-10x &= 1-6+4-3 \\
-2x &= -4 \\
x &= \frac{-4}{-2} \\
\mathbf{x} &\mathbf{= 2}
\end{aligned}$$
$$\begin{aligned}
2(x-3)+7 &= 6x-5(1+2x) \\
2x-6+7 &= 6x-5-10x \\
2x-6x+10x &= -5+6-7 \\
6x &= -6 \\
x &= \frac{-6}{6} \\
\mathbf{x} &\mathbf{= -1}
\end{aligned}$$
Ejercicios
Bloque 1
$6-5(3x-1)=-9+5(4x+2)$
$6(x+2)-3=4x-2(4-5x)$
$-2+3(4+7x)=1-3(x-6)$
$6(x+2)-3=4x-2(4-5x)$
$-2+3(4+7x)=1-3(x-6)$
Bloque 2
$2(-5x+7)+9=8x-4(1+6x)$
$3x-4(x-1)=5(2x+3)-10$
$-3(-2x-8)+6=7x+5(4-2x)$
$3x-4(x-1)=5(2x+3)-10$
$-3(-2x-8)+6=7x+5(4-2x)$
Respuestas
▼Bloque 1
$$\begin{aligned}
6-5(3x-1) &= -9+5(4x+2) \\
6-15x+5 &= -9+20x+10 \\
-15x-20x &= -9+10-6-5 \\
-35x &= -10 \\
x &= \frac{-10}{-35} \\
\mathbf{x} &\mathbf{= +\tfrac{2}{7}}
\end{aligned}$$
$$\begin{aligned}
6(x+2)-3 &= 4x-2(4-5x) \\
6x+12-3 &= 4x-8+10x \\
6x-4x-10x &= -8-12+3 \\
-8x &= -17 \\
x &= \frac{-17}{-8} \\
\mathbf{x} &\mathbf{= \tfrac{17}{8}}
\end{aligned}$$
Bloque 2
$$\begin{aligned}
2(-5x+7)+9 &= 8x-4(1+6x) \\
-10x+14+9 &= 8x-4-24x \\
-10x-8x+24x &= -14-9-4 \\
6x &= -27 \\
x &= \frac{-27}{6} \\
\mathbf{x} &\mathbf{= -\tfrac{9}{2}}
\end{aligned}$$
$$\begin{aligned}
3x-4(x-1) &= 5(2x+3)-10 \\
3x-4x+4 &= 10x+15-10 \\
3x-4x-10x &= 15-10-4 \\
-11x &= 1 \\
\mathbf{x} &\mathbf{= -\tfrac{1}{11}}
\end{aligned}$$