1ºBACH CCSS ECUACIONES, INECUACIONES Y SISTEMAS (ACTIVIDADES)

Ecuaciones, inecuaciones y sistemas

Actividades

1. $\displaystyle{3^{x}}=27$
2. $\displaystyle{7^{x+1}}=1$
3. $\displaystyle{5^{x-1}}=25$
4. $\displaystyle{2^{x}}=\displaystyle{\frac{1}{8}}$
5. $\displaystyle{2^{x+1}}+\displaystyle{2^{x}}+\displaystyle{2^{x-1}}=14$
6. $\displaystyle{6^{2x}}=1296$
7. $\displaystyle{2^{x^2-1}}=8$
8. $\displaystyle{3^{x}} \cdot \displaystyle{9^{x}}=\displaystyle{9^{3}}$
9. $\displaystyle{2^{5-x^2}}=\displaystyle{\frac{1}{16}}$
10. $\displaystyle{5^{x+3}}=\displaystyle{\sqrt{125}}$
11. $\displaystyle{3^{x+1}}+\displaystyle{3^{x}}+\displaystyle{3^{x-1}}=39$
12. $\displaystyle{2^{x+1}}+\displaystyle{2^{x}}+\displaystyle{2^{x-1}}=28$
13. $\displaystyle{2^{2x}}-5 \cdot \displaystyle{2^{x}}+4=0$
14. $\displaystyle{4^{x}}-3 \cdot \displaystyle{2^{x+1}}+8=0$
15. $\displaystyle{2^{x}}+\displaystyle{2^{1-x}}=3$
16. $\displaystyle{2^{x-1}}+\displaystyle{\frac{1}{2^{x-3}}}=5$
17. $\displaystyle{log(x)}+\displaystyle{log(5)}=2$
18. $\displaystyle{log(x)}+\displaystyle{log(x+3)}=2\displaystyle{log(x+1)}$
19. $\displaystyle{log_{x}(16)}=2$
20. $\displaystyle{log(x)}+\displaystyle{log(80)}=3$
21. $\displaystyle{log(22-x)}=-1+\displaystyle{log(x)}$
22. $\displaystyle{log(x^2)}-\displaystyle{log(3)}=\displaystyle{log(x)}+\displaystyle{log(5)}$
23. $2\displaystyle{log(x)}=4+\displaystyle{log\left(\frac{x}{10}\right)}$
24. $\left\{\begin{array}{l} 3x-1 \geq 7-x\\ 1-x \leq 1-2x \end{array}\right.$
25. $\left\{\begin{array}{l} x \leq 2\\ x \geq 6 \end{array}\right.$
26. $\left\{\begin{array}{l} 2x-3 \leq 6-x\\ 4-2x > 6 \end{array}\right.$
27. $\left\{\begin{array}{l} \displaystyle{\frac{x}{2}}+1 > 2\\ 5+x \geq 2x \end{array}\right.$
28. $\left\{\begin{array}{l} x^2 +3 \leq 7\\ x-1 \geq 0 \end{array}\right.$
29. $\left\{\begin{array}{l} x^2-7x+6 \leq 0\\ -x^2+8x > 7 \end{array}\right.$
30. $\left\{\begin{array}{l} \displaystyle{\frac{x-2}{3}} - \displaystyle{\frac{3x-1}{5}} \leq \displaystyle{\frac{17}{15}}\\ 8-3x \geq 2-x \end{array}\right.$
31. $x+y > 3$
32. $x + \displaystyle{\frac{y}{4}} > 1$
33. $3x-y \leq 2$
34. $x+1 \geq y$
35. $\left\{\begin{array}{l} x+2y+z=0\\ 2x-z=1\\ 3x-y-2z=3 \end{array}\right.$
36. $\left\{\begin{array}{l} 2x+y-z=5\\ x+2y+z=4\\ x-y=1 \end{array}\right.$
37. $\left\{\begin{array}{l} x+2y=1\\ 2x-z=1\\ 5y+z=0 \end{array}\right.$
38. $\left\{\begin{array}{l} x+4y+3z=-1\\ 2x-3y-2z=1\\ -x+2y+4z=2 \end{array}\right.$
39. $\left\{\begin{array}{l} 2x+y+z=55\\ x+2y+z=45\\ x+y+2z=40 \end{array}\right.$
40. $\left\{\begin{array}{l} x+y+z=45\\ 13x+12y+8z=430\\ 2x+2y-z=0 \end{array}\right.$

Soluciones:

1. $x=3$
2. $x=-1$
3. $x=3$
4. $x=-3$
5. $x=2$
6. $x=2$
7. $x=\pm 2$
8. $x=2$
9. $x=\pm 3$
10. $x=\displaystyle{-\frac{3}{2}}$
11. $x=2$
12. $x=3$
13. $x=0, x=2$
14. $x=1, x=2$
15. $x=0, x=1$
16. $x=1, x=3$
17. $x=20$
18. $x=1$
19. $x=4$
20. $x=\displaystyle{\frac{25}{2}}$
21. $x=20$
22. $x=15$
23. $x=1000$
24. No tienen solución
25. No tienen solución
26. $(-\infty,-1)$
27. $(2,5]$
28. $[1,2]$
29. $(1,6]$
30. $[-6,3]$
31. 
32. 
33. 
34. 
35. $x=3, y=-4, z=5$
36. $x=2, y=1, z=0$
37. $x=3, y=-1, z=5$
38. $x=0, y=-1, z=1$
39. $x=20, y=10, z=5$
40. $x=10, y=5, z=30$