EJERCICIOS

1. \(2x = 18\)
2. \(-4x = 12\)
3. \(x - 5 = 3\)
4. \(3 - x = 7\)
5. \(2x - 6 = 8\)
6. \(-3x + 2 = -9\)
7. \(-5x - 2 = -18\)
8. \(-(x-3) + 6 = 0\)
9. \(-(2x+9) = 15\)
10. \(2(x+3) = 0\)
11. \(4(6+x) = 40\)
12. \(-3(5 - x) = -60\)
13. \(-2(2x - 10) = 100\)
14. \(2(6 - x) = 36\)
15. \(3x + 6 = x + 50\)
16. \(4x + 7 - 2x + 29 = 0\)
17. \;2(x - 6) + 3(x + 7) = 0\)
18. \;5(x - 4) = 3(x - 6)\)
19. \(\dfrac{x}{7} = 2\)
20. \(\dfrac{x}{5} = 3\)
21. \(\dfrac{x}{2} + 6 = 0\)
22. \(\dfrac{x}{-3} + 4 = 16\)
23. \(\dfrac{x - 8}{2} = 20\)
24. \(\dfrac{2x - 1}{-2} = 5\)
25. \(\dfrac{x}{3} + \dfrac{x}{2} = 10\)
26. \(\dfrac{x - 1}{4} - \dfrac{x + 1}{2} = 7\)
27. \(\dfrac{1}{8} + \dfrac{2x + 3}{4} = -\dfrac{x}{2}\)
28. \(\dfrac{2x + 3}{2} = \dfrac{3x + 1}{3}\)

//////////////////////////////////////

Ecuaciones: desarrollo

1. \[ \begin{aligned} 2x&=18\\ x&=\frac{18}{2}=9 \end{aligned} \]
2. \[ \begin{aligned} -4x&=12\\ x&=\frac{12}{-4}=-3 \end{aligned} \]
3. \[ \begin{aligned} x-5&=3\\ x&=3+5=8 \end{aligned} \]
4. \[ \begin{aligned} 3-x&=7\\ -x&=7-3=4\\ x&=-4 \end{aligned} \]
5. \[ \begin{aligned} 2x-6&=8\\ 2x&=14\\ x&=7 \end{aligned} \]
6. \[ \begin{aligned} -3x+2&=-9\\ -3x&=-11\\ x&=\frac{-11}{-3}=\frac{11}{3} \end{aligned} \]
7. \[ \begin{aligned} -5x-2&=-18\\ -5x&=-16\\ x&=\frac{-16}{-5}=\frac{16}{5} \end{aligned} \]
8. \[ \begin{aligned} -(x-3)+6&=0\\ -x+3+6&=0\\ -x+9&=0\\ x&=9 \end{aligned} \]
9. \[ \begin{aligned} -(2x+9)&=15\\ -2x-9&=15\\ -2x&=24\\ x&=-12 \end{aligned} \]
10. \[ \begin{aligned} 2(x+3)&=0\\ 2x+6&=0\\ 2x&=-6\\ x&=-3 \end{aligned} \]
11. \[ \begin{aligned} 4(6+x)&=40\\ 24+4x&=40\\ 4x&=16\\ x&=4 \end{aligned} \]
12. \[ \begin{aligned} -3(5-x)&=-60\\ -15+3x&=-60\\ 3x&=-45\\ x&=-15 \end{aligned} \]
13. \[ \begin{aligned} -2(2x-10)&=100\\ -4x+20&=100\\ -4x&=80\\ x&=-20 \end{aligned} \]
14. \[ \begin{aligned} 2(6-x)&=36\\ 12-2x&=36\\ -2x&=24\\ x&=-12 \end{aligned} \]
15. \[ \begin{aligned} 3x+6&=x+50\\ 3x-x&=50-6\\ 2x&=44\\ x&=22 \end{aligned} \]
16. \[ \begin{aligned} 4x+7-2x+29&=0\\ 2x+36&=0\\ 2x&=-36\\ x&=-18 \end{aligned} \]
17. \[ \begin{aligned} 2(x-6)+3(x+7)&=0\\ 2x-12+3x+21&=0\\ 5x+9&=0\\ 5x&=-9\\ x&=-\frac{9}{5} \end{aligned} \]
18. \[ \begin{aligned} 5(x-4)&=3(x-6)\\ 5x-20&=3x-18\\ 5x-3x&=-18+20\\ 2x&=2\\ x&=1 \end{aligned} \]
19. \[ \begin{aligned} \frac{x}{7}&=2\\ x&=14 \end{aligned} \]
20. \[ \begin{aligned} \frac{x}{5}&=3\\ x&=15 \end{aligned} \]
21. \[ \begin{aligned} \frac{x}{2}+6&=0\\ \frac{x}{2}&=-6\\ x&=-12 \end{aligned} \]
22. \[ \begin{aligned} \frac{x}{-3}+4&=16\\ \frac{x}{-3}&=12\\ x&=-36 \end{aligned} \]
23. \[ \begin{aligned} \frac{x-8}{2}&=20\\ x-8&=40\\ x&=48 \end{aligned} \]
24. \[ \begin{aligned} \frac{2x-1}{-2}&=5\\ 2x-1&=-10\\ 2x&=-9\\ x&=-\frac{9}{2} \end{aligned} \]
25. \[ \begin{aligned} \frac{x}{3}+\frac{x}{2}&=10\\ \text{(mcm \(=6\)): } 2x+3x&=60\\ 5x&=60\\ x&=12 \end{aligned} \]
26. \[ \begin{aligned} \frac{x-1}{4}-\frac{x+1}{2}&=7\\ \text{(den. \(4\)): } (x-1)-2(x+1)&=28\\ x-1-2x-2&=28\\ -x-3&=28\\ -x&=31\\ x&=-31 \end{aligned} \]
27. \[ \begin{aligned} \frac{1}{8}+\frac{2x+3}{4}&=-\frac{x}{2}\\ \text{(den. \(8\)): } 1+2(2x+3)&=-4x\\ 1+4x+6&=-4x\\ 4x+7&=-4x\\ 8x&=-7\\ x&=-\frac{7}{8} \end{aligned} \]
28. \[ \begin{aligned} \frac{2x+3}{2}&=\frac{3x+1}{3}\\ 3(2x+3)&=2(3x+1)\\ 6x+9&=6x+2\\ 9&=2\quad\Rightarrow\quad \text{contradicción} \end{aligned} \] \(\Rightarrow\) **Sin solución** (ecuación inconsistente).