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CAPITULO VIII

Ecuaciones enteras de primer grado

Ejercicio 79

Resolver las siguientes ecuaciones:

$\begin{matrix} x - (2 x + 1) & = 8 - (3 x + 3) \\ x - 2 x - 1 & = 8 - 3 x - 3 \\ - x - 1 & = - 3 x + 5 \\ - x + 3 x & = 5 + 1 \\ 2 x & = 6 \\ x & = \frac{}{2} \\ x & = 3 \end{matrix}$
$\begin{matrix} 15 x - 10 & = 6 x - (x + 2) + (- x + 3) \\ 15 x - 10 & = 6 x - x - 2 - x + 3 \\ 15 x - 10 & = 4 x + 1 \\ 15 x - 4 x & = 10 + 1 \\ 11 x & = 11 \\ x & = \frac{11}{11} \\ x & = 1 \end{matrix}$
$\begin{matrix} (5 - 3 x) - (- 4 x + 6) & = (8 x + 11) - (3 x - 6) \\ 5 - 3 x + 4 x - 6 & = 8 x + 11 - 3 x + 6 \\ x - 1 & = 5 x + 17 \\ x - 5 x & = 17 + 1 \\ - 4 x & = 18 \\ x & = - \frac{}{} \\ x & = - \frac{9}{2} \end{matrix}$
$\begin{matrix} 30 x - (- x + 6) + (- 5 x + 4) & = - (5 x + 6) + (- 8 + 3 x) \\ 30 x + x - 6 - 5 x + 4 & = - 5 x - 6 - 8 + 3 x \\ 26 x - 2 & = - 2 x - 14 \\ 26 x + 2 x & = 2 - 14 \\ 28 x & = - 12 \\ x & = - \frac{}{} \\ x & = - \frac{3}{7} \end{matrix}$
$\begin{matrix} 15 x + (- 6 x + 5) - 2 - (- x + 3) & = - (7 x + 23) - x + (3 - 2 x) \\ 15 x - 6 x + 5 - 2 + x - 3 & = - 7 x - 23 - x + 3 - 2 x \\ 10 x & = - 10 x - 20 \\ 10 x + 10 x & = - 20 \\ 20 x & = - 20 \\ x & = - \frac{20}{20} \\ x & = - 1 \end{matrix}$
$\begin{matrix} 3 x + [- 5 x - (x + 3)] & = 8 x + (- 5 x - 9) \\ 3 x + [- 5 x - x - 3] & = 8 x - 5 x - 9 \\ 3 x - 5 x - x - 3 & = 3 x - 9 \\ - 3 x & = 3 x - 9 + 3 \\ - 3 x - 3 x & = - 6 \\ - 6 x & = - 6 \\ x & = \frac{- 6}{- 6} \\ x & = 1 \end{matrix}$
$\begin{matrix} 16 x - [3 x - (6 - 9 x)] & = 30 x + [- (3 x + 2) - (x + 3)] \\ 16 x - [3 x - 6 + 9 x] & = 30 x + [- 3 x - 2 - x - 3] \\ 16 x - 12 x + 6 & = 30 x - 4 x - 5 \\ 4 x + 6 & = 26 x - 5 \\ 4 x - 26 x & = - 6 - 5 \\ - 22 x & = - 11 \\ x & = \frac{- 11}{-} \\ x & = \frac{1}{2} \end{matrix}$
$\begin{matrix} x - [5 + 3 x - {5 x - (6 + x)}] & = - 3 \\ x - [5 + 3 x - {5 x - 6 - x}] & = - 3 \\ x - [5 + 3 x - 4 x + 6] & = - 3 \\ x - (11 - x) & = - 3 \\ x - 11 + x & = - 3 \\ 2 x & = 11 - 3 \\ 2 x & = 8 \\ x & = \frac{}{2} \\ x & = 4 \end{matrix}$
$\begin{matrix} 9 x - (5 x + 1) - {2 + 8 x - (7 x - 5)} + 9 x & = 0 \\ 18 x - 5 x - 1 - {2 + 8 x - 7 x + 5} & = 0 \\ 13 x - 1 - (x + 7) & = 0 \\ 13 x - 1 - x - 7 & = 0 \\ 12 x - 8 & = 0 \\ 12 x & = 8 \\ x & = \frac{}{} \\ x & = \frac{2}{3} \end{matrix}$
$\begin{matrix} 71 + [- 5 x + (- 2 x + 3)] & = 25 - [- (3 x + 4) - (4 x + 3)] \\ 71 + [- 5 x - 2 x + 3] & = 25 - [- 3 x - 4 - 4 x - 3] \\ 71 - 7 x + 3 & = 25 - (- 7 x - 7) \\ 74 - 7 x & = 25 + 7 x + 7 \\ - 7 x - 7 x & = 32 - 74 \\ - 14 x & = - 42 \\ x & = \frac{-}{- 14} \\ x & = 3 \end{matrix}$
$\begin{matrix} - {3 x + 8 - [- 15 + 6 x - (- 3 x + 2) - (5 x + 4)] - 29} & = - 5 \\ - {3 x + 8 - [- 15 + 6 x + 3 x - 2 - 5 x - 4] - 29} & = - 5 \\ - {3 x + 8 - [4 x - 21] - 29} & = - 5 \\ - {3 x + 8 - 4 x + 21 - 29} & = - 5 \\ - {- x} & = - 5 \\ x & = - 5 \end{matrix}$