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. \(x=10, y=5, z=30\)