Ejercicio 80 – Solucionario Baldor

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DESCARGA

CAPITULO VIII

Ecuaciones enteras de primer grado

Ejercicio 80

Resolver las siguientes ecuaciones:

$\begin{matrix} x + 3 (x - 1) & = 6 - 4 (2 x + 3) \\ x + 3 x - 3 & = 6 - 8 x - 12 \\ 4 x - 3 & = - 6 - 8 x \\ 4 x + 8 x & = 3 - 6 \\ 12 x & = - 3 \\ x & = - \frac{3}{} \\ x & = - \frac{1}{4} \end{matrix}$
$\begin{matrix} 5 (x - 1) + 16 (2 x + 3) & = 3 (2 x - 7) - x \\ 5 x - 5 + 32 x + 48 & = 6 x - 21 - x \\ 37 x + 43 & = 5 x - 21 \\ 37 x - 5 x & = - 43 - 21 \\ 32 x & = - 64 \\ x & = - \frac{}{32} \\ x & = - 2 \end{matrix}$
$\begin{matrix} 2 (3 x + 3) - 4 (5 x - 3) & = x (x - 3) - x (x + 5) \\ 6 x + 6 - 20 x + 12 & = x^{2} - 3 x - x^{2} - 5 x \\ - 14 x + 18 & = - 8 x \\ - 14 x + 8 x & = - 18 \\ - 6 x & = - 18 \\ x & = \frac{-}{- 6} \\ x & = 3 \end{matrix}$
$\begin{matrix} 184 - 7 (2 x + 5) & = 301 + 6 (x - 1) - 6 \\ 184 - 14 x - 35 & = 301 + 6 x - 6 - 6 \\ - 14 x + 149 & = 289 + 6 x \\ - 14 x - 6 x & = 289 - 149 \\ - 20 x & = 140 \\ x & = - \frac{}{20} \\ x & = - 7 \end{matrix}$
$\begin{matrix} 7 (18 - x) - 6 (3 - 5 x) & = - (7 x + 9) - 3 (2 x + 5) - 12 \\ 126 - 7 x - 18 + 30 x & = - 7 x - 9 - 6 x - 15 - 12 \\ 23 x + 108 & = - 13 x - 36 \\ 23 x + 13 x & = - 108 - 36 \\ 36 x & = - 144 \\ x & = \frac{-}{36} \\ x & = - 4 \end{matrix}$
$\begin{matrix} 3 x (x - 3) + 5 (x + 7) - x (x + 1) - 2 (x^{2} + 7) + 4 & = 0 \\ 3 x^{2} - 9 x + 5 x + 35 - x^{2} - x - 2 x^{2} - 14 + 4 & = 0 \\ - 5 x + 25 & = 0 \\ - 5 x & = - 25 \\ x & = \frac{-}{- 5} \\ x & = 5 \end{matrix}$
$\begin{matrix} - 3 (2 x + 7) + (- 5 x + 6) - 8 (1 - 2 x) - (x - 3) & = 0 \\ - 6 x - 21 - 5 x + 6 - 8 + 16 x - x + 3 & = 0 \\ 4 x - 20 & = 0 \\ 4 x & = 20 \\ x & = \frac{}{4} \\ x & = 5 \end{matrix}$
$\begin{matrix} (3 x - 4) (4 x - 3) & = (6 x - 4) (2 x - 5) \\ 12 x^{2} - 9 x - 16 x + 12 & = 12 x^{2} - 30 x - 8 x + 20 \\ - 25 x + 12 & = - 38 x + 20 \\ 38 x - 25 x & = 20 - 12 \\ 13 x & = 8 \\ x & = \frac{8}{13} \end{matrix}$
$\begin{matrix} (4 - 5 x) (4 x - 5) & = (10 x - 3) (7 - 2 x) \\ 16 x - 20 - 20 x^{2} + 25 x & = 70 x - 20 x^{2} - 21 + 6 x \\ 41 x - 20 & = 76 x - 21 \\ 41 x - 76 x & = 20 - 21 \\ - 35 x & = - 1 \\ x & = \frac{1}{35} \end{matrix}$
$\begin{matrix} (x + 1) (2 x + 5) & = (2 x + 3) (x - 4) + 5 \\ 2 x^{2} + 5 x + 2 x + 5 & = 2 x^{2} - 8 x + 3 x - 12 + 5 \\ 7 x + 5 & = - 5 x - 7 \\ 7 x + 5 x & = - 7 - 5 \\ 12 x & = - 12 \\ x & = - \frac{12}{12} \\ x & = - 1 \end{matrix}$
$\begin{matrix} {(x - 2)}^{2} - {(3 - x)}^{2} & = 1 \\ [(x - 2) + (3 - x)] [(x - 2) - (3 - x)] & = 1 \\ [x - 2 + 3 - x] [x - 2 - 3 + x] & = 1 \\ 2 x - 5 & = 1 \\ 2 x & = 5 + 1 \\ x & = \frac{}{2} \\ x & = 3 \end{matrix}$
$\begin{matrix} 14 - (5 x - 1) (2 x + 3) & = 17 - (10 x + 1) (x - 6) \\ 14 - (10 x^{2} + 15 x - 2 x - 3) & = 17 - (10 x^{2} - 60 x + x - 6) \\ 14 - 10 x^{2} - 15 x + 2 x + 3 & = 17 - 10 x^{2} + 60 x - x + 6 \\ - 13 x + 17 & = 59 x + 23 \\ - 13 x - 59 x & = 23 - 17 \\ - 72 x & = 6 \\ x & = - \frac{6}{} \\ x & = - \frac{1}{12} \end{matrix}$
$\begin{matrix} {(x - 2)}^{2} + x (x - 3) & = 3 (x + 4) (x - 3) - (x + 2) (x - 1) + 2 \\ x^{2} - 4 x + 4 + x^{2} - 3 x & = 3 (x^{2} + x - 12) - (x^{2} + x - 2) + 2 \\ 2 x^{2} - 7 x + 4 & = 3 x^{2} + 3 x - 36 - x^{2} - x + 2 + 2 \\ 2 x^{2} - 7 x & = 2 x^{2} + 2 x - 36 \\ - 7 x - 2 x & = - 36 \\ - 9 x & = - 36 \\ x & = \frac{-}{- 9} \\ x & = 4 \end{matrix}$
$\begin{matrix} {(3 x - 1)}^{2} - 5 (x - 2) - {(2 x + 3)}^{2} - (5 x + 2) (x - 1) & = 0 \\ 9 x^{2} - 6 x + 1 - 5 x + 10 - (4 x^{2} + 12 x + 9) - (5 x^{2} - 5 x + 2 x - 2) & = 0 \\ 9 x^{2} - 11 x + 11 - 4 x^{2} - 12 x - 9 - 5 x^{2} + 3 x + 2 & = 0 \\ - 20 x + 4 & = 0 \\ x & = \frac{- 4}{-} \\ x & = \frac{1}{5} \end{matrix}$
$\begin{matrix} 2 {(x - 3)}^{2} - 3 {(x + 1)}^{2} + (x - 5) (x - 3) + 4 (x^{2} - 5 x + 1) & = 4 x^{2} - 12 \\ 2 (x^{2} - 6 x + 9) - 3 (x^{2} + 2 x + 1) + (x^{2} - 8 x + 15) + 4 x^{2} - 20 x + 4 & = 4 x^{2} - 12 \\ 2 x^{2} - 12 x + 18 - 3 x^{2} - 6 x - 3 + x^{2} - 8 x + 15 - 20 x + 4 & = - 12 \\ - 46 x + 34 & = - 12 \\ - 46 x & = - 34 - 12 \\ x & = \frac{- 46}{- 46} \\ x & = 1 \end{matrix}$
$\begin{matrix} 5 {(x - 2)}^{2} - 5 {(x + 3)}^{2} + (2 x - 1) (5 x + 2) - 10 x^{2} & = 0 \\ 5 (x^{2} - 4 x + 4) - 5 (x^{2} + 6 x + 9) + (10 x^{2} + 4 x - 5 x - 2) - 10 x^{2} & = 0 \\ 5 x^{2} - 20 x + 20 - 5 x^{2} - 30 x - 45 + 10 x^{2} - x - 2 - 10 x^{2} & = 0 \\ - 51 x - 27 & = 0 \\ - 51 x & = 27 \\ x & = - \frac{}{} \\ x & = - \frac{9}{17} \end{matrix}$
$\begin{matrix} x^{2} - 5 x + 15 & = x (x - 3) - 14 + 5 (x - 2) + 3 (13 - 2 x) \\ x^{2} - 5 x + 15 & = x^{2} - 3 x - 14 + 5 x - 10 + 39 - 6 x \\ - 5 x + 15 & = - 4 x + 15 \\ - 5 x + 4 x & = 0 \\ - x & = 0 \\ x & = 0 \end{matrix}$
$\begin{matrix} 3 (5 x - 6) (3 x + 2) - 6 (3 x + 4) (x - 1) - 3 (9 x + 1) (x - 2) & = 0 \\ D i v i d i e n d o l a e c u a c i ó n p a r a 3 \\ (5 x - 6) (3 x + 2) - 2 (3 x + 4) (x - 1) - (9 x + 1) (x - 2) & = 0 \\ (15 x^{2} + 10 x - 18 x - 12) - 2 (3 x^{2} - 3 x + 4 x - 4) - (9 x^{2} - 18 x + x - 2) & = 0 \\ 15 x^{2} - 8 x - 12 - 6 x^{2} - 2 x + 8 - 9 x^{2} + 17 x + 2 & = 0 \\ 7 x - 2 & = 0 \\ 7 x & = 2 \\ x & = \frac{2}{7} \end{matrix}$
$\begin{matrix} 7 {(x - 4)}^{2} - 3 {(x + 5)}^{2} & = 4 (x + 1) (x - 1) - 2 \\ 7 (x^{2} - 8 x + 16) - 3 (x^{2} + 10 x + 25) & = 4 (x^{2} - 1) - 2 \\ 7 x^{2} - 56 x + 112 - 3 x^{2} - 30 x - 75 & = 4 x^{2} - 4 - 2 \\ 4 x^{2} - 86 x + 37 & = 4 x^{2} - 6 \\ - 86 x & = - 37 - 6 \\ - 86 x & = - 43 \\ x & = \frac{- 43}{-} \\ x & = \frac{1}{2} \end{matrix}$
$\begin{matrix} 5 {(1 - x)}^{2} - 6 (x^{2} - 3 x - 7) & = x (x - 3) - 2 x (x + 5) - 2 \\ 5 (1 - 2 x + x^{2}) - 6 x^{2} + 18 x + 42 & = x^{2} - 3 x - 2 x^{2} - 10 x - 2 \\ 5 - 10 x + 5 x^{2} - 6 x^{2} + 18 x + 42 & = - x^{2} - 13 x - 2 \\ - x^{2} + 8 x + 47 & = - x^{2} - 13 x - 2 \\ 8 x + 13 x & = - 47 - 2 \\ 21 x & = - 49 \\ x & = - \frac{}{} \\ x & = - \frac{7}{3} \end{matrix}$