2. Реши уравнения: a) $x + \frac{x}{10} = -\frac{11}{2}$ б) $\frac{x}{5} + \frac{x}{9} = -\frac{14}{15}$ в) $(x-6)^2 = (x-3)^2$ г) $\frac{26}{35} = \frac{x}{770}$ д) $\frac{x}{49} = \frac{544}{784}$

Question

$Фото задания: 2. Реши уравнения: a) $x + \frac{x}{10} = -\frac{11}{2}$ б) $\frac{x}{5} + \frac{x}{9} = -\frac{14}{15}$ в) \((x-6)^2 =…$ Фото задания

Accepted Answer

$\textbf{а)}$ \[ x + \frac{x}{10} = -\frac{11}{2} \] \[ \frac{10x + x}{10} = -\frac{11}{2} \] \[ \frac{11x}{10} = -\frac{11}{2} \] \[ x = -\frac{11}{2} \cdot \frac{10}{11} \] \[ x = -\frac{10}{2} \] \[ x = -5 \] $\textbf{Ответ: } x = -5$
$\textbf{б)}$ \[ \frac{x}{5} + \frac{x}{9} = -\frac{14}{15} \] \[ \frac{9x + 5x}{45} = -\frac{14}{15} \] \[ \frac{14x}{45} = -\frac{14}{15} \] \[ x = -\frac{14}{15} \cdot \frac{45}{14} \] \[ x = -\frac{45}{15} \] \[ x = -3 \] $\textbf{Ответ: } x = -3$
$\textbf{в)}$ \[ (x-6)^2 = (x-3)^2 \] \[ x^2 - 12x + 36 = x^2 - 6x + 9 \] \[ -12x + 36 = -6x + 9 \] \[ 36 - 9 = -6x + 12x \] \[ 27 = 6x \] \[ x = \frac{27}{6} \] \[ x = \frac{9}{2} \] $\textbf{Ответ: } x = \frac{9}{2}$
$\textbf{г)}$ \[ \frac{26}{35} = \frac{x}{770} \] \[ x = \frac{26}{35} \cdot 770 \] \[ x = 26 \cdot \frac{770}{35} \] \[ x = 26 \cdot 22 \] \[ x = 572 \] $\textbf{Ответ: } x = 572$
$\textbf{д)}$ \[ \frac{x}{49} = \frac{544}{784} \] \[ x = \frac{544}{784} \cdot 49 \] \[ x = 544 \cdot \frac{49}{784} \] \[ x = 544 \cdot \frac{1}{16} \] \[ x = \frac{544}{16} \] \[ x = 34 \] $\textbf{Ответ: } x = 34$

2. Реши уравнения: a) \(x + \frac{x}{10} = -\frac{11}{2}\) б) \(\frac{x}{5} + \frac{x}{9} = -\frac{14}{15}\) в) \((x-6)^2 = (x-3)^2\) г) \(\frac{26}{35} = \frac{x}{770}\) д) \(\frac{x}{49} = \frac{544}{784}\)