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CAPITULO VIII

Ejercicio 80
Resolver las siguientes ecuaciones:
1. $\begin{array}{cc}x+3\left(x–1\right)& =6–4\left(2x+3\right)\\ & \\ x+3x–3& =6–8x–12\\ 4x–3& =–6–8x\\ 4x+8x& =3–6\\ 12x& =–3\\ x& =–\frac{\overline{)3}}{}\\ x& =–\frac{1}{4}\end{array}$
2. $\begin{array}{cc}5\left(x–1\right)+16\left(2x+3\right)& =3\left(2x–7\right)–x\\ & \\ 5x–5+32x+48& =6x–21–x\\ 37x+43& =5x–21\\ 37x–5x& =–43–21\\ 32x& =–64\\ x& =–\frac{}{\overline{)32}}\\ x& =–2\end{array}$
3. $\begin{array}{cc}2\left(3x+3\right)–4\left(5x–3\right)& =x\left(x–3\right)–x\left(x+5\right)\\ & \\ 6x+6–20x+12& =\overline{){x}^{2}}–3x–\overline{){x}^{2}}–5x\\ –14x+18& =–8x\\ –14x+8x& =–18\\ –6x& =–18\\ x& =\frac{–}{–\overline{)6}}\\ x& =3\end{array}$
4. $\begin{array}{cc}184–7\left(2x+5\right)& =301+6\left(x–1\right)–6\\ & \\ 184–14x–35& =301+6x–6–6\\ –14x+149& =289+6x\\ –14x–6x& =289–149\\ –20x& =140\\ x& =–\frac{}{\overline{)20}}\\ x& =–7\end{array}$
5. $\begin{array}{cc}7\left(18–x\right)–6\left(3–5x\right)& =–\left(7x+9\right)–3\left(2x+5\right)–12\\ & \\ 126–7x–18+30x& =–7x–9–6x–15–12\\ 23x+108& =–13x–36\\ 23x+13x& =–108–36\\ 36x& =–144\\ x& =\frac{–}{\overline{)36}}\\ x& =–4\end{array}$
6. $\begin{array}{cc}3x\left(x–3\right)+5\left(x+7\right)–x\left(x+1\right)–2\left({x}^{2}+7\right)+4& =0\\ & \\ \overline{)3{x}^{2}}–9x+5x+35–\overline{){x}^{2}}–x–\overline{)2{x}^{2}}–14+4& =0\\ –5x+25& =0\\ –5x& =–25\\ x& =\frac{–}{–\overline{)5}}\\ x& =5\end{array}$
7. $\begin{array}{cc}–3\left(2x+7\right)+\left(–5x+6\right)–8\left(1–2x\right)–\left(x–3\right)& =0\\ & \\ –6x–21–5x+6–8+16x–x+3& =0\\ 4x–20& =0\\ 4x& =20\\ x& =\frac{}{\overline{)4}}\\ x& =5\end{array}$
8. $\begin{array}{cc}\left(3x–4\right)\left(4x–3\right)& =\left(6x–4\right)\left(2x–5\right)\\ & \\ \overline{)12{x}^{2}}–9x–16x+12& =\overline{)12{x}^{2}}–30x–8x+20\\ –25x+12& =–38x+20\\ 38x–25x& =20–12\\ 13x& =8\\ x& =\frac{8}{13}\end{array}$
9. $\begin{array}{cc}\left(4–5x\right)\left(4x–5\right)& =\left(10x–3\right)\left(7–2x\right)\\ & \\ 16x–20–\overline{)20{x}^{2}}+25x& =70x–\overline{)20{x}^{2}}–21+6x\\ 41x–20& =76x–21\\ 41x–76x& =20–21\\ –35x& =–1\\ x& =\frac{1}{35}\end{array}$
10. $\begin{array}{cc}\left(x+1\right)\left(2x+5\right)& =\left(2x+3\right)\left(x–4\right)+5\\ & \\ \overline{)2{x}^{2}}+5x+2x+5& =\overline{)2{x}^{2}}–8x+3x–12+5\\ 7x+5& =–5x–7\\ 7x+5x& =–7–5\\ 12x& =–12\\ x& =–\frac{\overline{)12}}{\overline{)12}}\\ x& =–1\end{array}$
11. $\begin{array}{cc}{\left(x–2\right)}^{2}–{\left(3–x\right)}^{2}& =1\\ & \\ \left[\left(x–2\right)+\left(3–x\right)\right]\left[\left(x–2\right)–\left(3–x\right)\right]& =1\\ \left[\overline{)x}–2+3–\overline{)x}\right]\left[x–2–3+x\right]& =1\\ 2x–5& =1\\ 2x& =5+1\\ x& =\frac{}{\overline{)2}}\\ x& =3\end{array}$
12. $\begin{array}{cc}14–\left(5x–1\right)\left(2x+3\right)& =17–\left(10x+1\right)\left(x–6\right)\\ & \\ 14–\left(10{x}^{2}+15x–2x–3\right)& =17–\left(10{x}^{2}–60x+x–6\right)\\ 14–\overline{)10{x}^{2}}–15x+2x+3& =17–\overline{)10{x}^{2}}+60x–x+6\\ –13x+17& =59x+23\\ –13x–59x& =23–17\\ –72x& =6\\ x& =–\frac{\overline{)6}}{}\\ x& =–\frac{1}{12}\end{array}$
13. $\begin{array}{cc}{\left(x–2\right)}^{2}+x\left(x–3\right)& =3\left(x+4\right)\left(x–3\right)–\left(x+2\right)\left(x–1\right)+2\\ & \\ {x}^{2}–4x+4+{x}^{2}–3x& =3\left({x}^{2}+x–12\right)–\left({x}^{2}+x–2\right)+2\\ 2{x}^{2}–7x+\overline{)4}& =3{x}^{2}+3x–36–{x}^{2}–x+\overline{)2}+\overline{)2}\\ \overline{)2{x}^{2}}–7x& =\overline{)2{x}^{2}}+2x–36\\ –7x–2x& =–36\\ –9x& =–36\\ x& =\frac{–}{–\overline{)9}}\\ x& =4\end{array}$
14. $\begin{array}{cc}{\left(3x–1\right)}^{2}–5\left(x–2\right)–{\left(2x+3\right)}^{2}–\left(5x+2\right)\left(x–1\right)& =0\\ & \\ 9{x}^{2}–6x+1–5x+10–\left(4{x}^{2}+12x+9\right)–\left(5{x}^{2}–5x+2x–2\right)& =0\\ \overline{)9{x}^{2}}–11x+11–\overline{)4{x}^{2}}–12x–9–\overline{)5{x}^{2}}+3x+2& =0\\ –20x+4& =0\\ x& =\frac{–\overline{)4}}{–}\\ x& =\frac{1}{5}\end{array}$
15. $\begin{array}{cc}2{\left(x–3\right)}^{2}–3{\left(x+1\right)}^{2}+\left(x–5\right)\left(x–3\right)+4\left({x}^{2}–5x+1\right)& =4{x}^{2}–12\\ & \\ 2\left({x}^{2}–6x+9\right)–3\left({x}^{2}+2x+1\right)+\left({x}^{2}–8x+15\right)+\overline{)4{x}^{2}}–20x+4& =\overline{)4{x}^{2}}–12\\ \overline{)2{x}^{2}}–12x+18–\overline{)3{x}^{2}}–6x–3+\overline{){x}^{2}}–8x+15–20x+4& =–12\\ –46x+34& =–12\\ –46x& =–34–12\\ x& =\frac{–\overline{)46}}{–\overline{)46}}\\ x& =1\end{array}$
16. $\begin{array}{cc}5{\left(x–2\right)}^{2}–5{\left(x+3\right)}^{2}+\left(2x–1\right)\left(5x+2\right)–10{x}^{2}& =0\\ & \\ 5\left({x}^{2}–4x+4\right)–5\left({x}^{2}+6x+9\right)+\left(10{x}^{2}+4x–5x–2\right)–10{x}^{2}& =0\\ \overline{)5{x}^{2}}–20x+20–\overline{)5{x}^{2}}–30x–45+\overline{)10{x}^{2}}–x–2–\overline{)10{x}^{2}}& =0\\ –51x–27& =0\\ –51x& =27\\ x& =–\frac{}{}\\ x& =–\frac{9}{17}\end{array}$
17. $\begin{array}{cc}{x}^{2}–5x+15& =x\left(x–3\right)–14+5\left(x–2\right)+3\left(13–2x\right)\\ & \\ \overline{){x}^{2}}–5x+15& =\overline{){x}^{2}}–3x–14+5x–10+39–6x\\ –5x+\overline{)15}& =–4x+\overline{)15}\\ –5x+4x& =0\\ –x& =0\\ x& =0\end{array}$
18. $\begin{array}{cc}7{\left(x–4\right)}^{2}–3{\left(x+5\right)}^{2}& =4\left(x+1\right)\left(x–1\right)–2\\ & \\ 7\left({x}^{2}–8x+16\right)–3\left({x}^{2}+10x+25\right)& =4\left({x}^{2}–1\right)–2\\ 7{x}^{2}–56x+112–3{x}^{2}–30x–75& =4{x}^{2}–4–2\\ \overline{)4{x}^{2}}–86x+37& =\overline{)4{x}^{2}}–6\\ –86x& =–37–6\\ –86x& =–43\\ x& =\frac{–\overline{)43}}{–}\\ x& =\frac{1}{2}\end{array}$
19. $\begin{array}{cc}5{\left(1–x\right)}^{2}–6\left({x}^{2}–3x–7\right)& =x\left(x–3\right)–2x\left(x+5\right)–2\\ & \\ 5\left(1–2x+{x}^{2}\right)–6{x}^{2}+18x+42& ={x}^{2}–3x–2{x}^{2}–10x–2\\ 5–10x+5{x}^{2}–6{x}^{2}+18x+42& =–{x}^{2}–13x–2\\ –\overline{){x}^{2}}+8x+47& =–\overline{){x}^{2}}–13x–2\\ 8x+13x& =–47–2\\ 21x& =–49\\ x& =–\frac{}{}\\ x& =–\frac{7}{3}\end{array}$