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7.7E: Mazoezi

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    176770

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    Kutatua usawa wa busara

    Katika mazoezi yafuatayo, tatua usawa wa kila busara na uandike suluhisho katika maelezo ya muda.

    1. \(\dfrac{x-3}{x+4} \geq 0\)

    Jibu

    \((-\infty,-4) \cup[3, \infty)\)

    2. \(\dfrac{x+6}{x-5} \geq 0\)

    3. \(\dfrac{x+1}{x-3} \leq 0\)

    Jibu

    \([-1,3)\)

    4. \(\dfrac{x-4}{x+2} \leq 0\)

    5. \(\dfrac{x-7}{x-1}>0\)

    Jibu

    \((-\infty, 1) \cup(7, \infty)\)

    6. \(\dfrac{x+8}{x+3}>0\)

    7. \(\dfrac{x-6}{x+5}<0\)

    Jibu

    \((-5,6)\)

    8. \(\dfrac{x+5}{x-2}<0\)

    9. \(\dfrac{3 x}{x-5}<1\)

    Jibu

    \(\left(-\dfrac{5}{2}, 5\right)\)

    10. \(\dfrac{5 x}{x-2}<1\)

    11. \(\dfrac{6 x}{x-6}>2\)

    Jibu

    \((-\infty,-3) \cup(6, \infty)\)

    12. \(\dfrac{3 x}{x-4}>2\)

    13. \(\dfrac{2 x+3}{x-6} \leq 1\)

    Jibu

    \([-9,6)\)

    14. \(\dfrac{4 x-1}{x-4} \leq 1\)

    15. \(\dfrac{3 x-2}{x-4} \geq 2\)

    Jibu

    \((-\infty,-6] \cup(4, \infty)\)

    16. \(\dfrac{4 x-3}{x-3} \geq 2\)

    17. \(\dfrac{1}{a}+\dfrac{2}{5}=\dfrac{1}{2}\)

    Jibu

    \(a=10\)

    18. \(\dfrac{1}{x^{2}-4 x-12}>0\)

    19. \(\dfrac{3}{x^{2}-5 x+4}<0\)

    Jibu

    \((1,4)\)

    20. \(\dfrac{4}{x^{2}+7 x+12}<0\)

    21. \(\dfrac{2}{2 x^{2}+x-15} \geq 0\)

    Jibu

    \((-\infty,-3) \cup\left(\dfrac{5}{2}, \infty\right)\)

    22. \(\dfrac{6}{3 x^{2}-2 x-5} \geq 0\)

    23. \(\dfrac{-2}{6 x^{2}-13 x+6} \leq 0\)

    Jibu

    \(\left(-\infty, \dfrac{2}{3}\right) \cup\left(\dfrac{3}{2}, \infty\right)\)

    24. \(\dfrac{-1}{10 x^{2}+11 x-6} \leq 0\)

    17. \(\dfrac{1}{a}+\dfrac{2}{5}=\dfrac{1}{2}\)

    Jibu

    \(a=10\)

    18. \(\dfrac{1}{x^{2}-4 x-12}>0\)

    19. \(\dfrac{3}{x^{2}-5 x+4}<0\)

    Jibu

    \((1,4)\)

    20. \(\dfrac{4}{x^{2}+7 x+12}<0\)

    25. \(\dfrac{1}{2}+\dfrac{12}{x^{2}}>\dfrac{5}{x}\)

    Jibu

    \((-\infty, 0) \cup(0,4) \cup(6, \infty)\)

    26. \(\dfrac{1}{3}+\dfrac{1}{x^{2}}>\dfrac{4}{3 x}\)

    27. \(\dfrac{1}{2}-\dfrac{4}{x^{2}} \leq \dfrac{1}{x}\)

    Jibu

    \([-2,0) \cup(0,4]\)

    28. \(\dfrac{1}{2}-\dfrac{3}{2 x^{2}} \geq \dfrac{1}{x}\)

    29. \(\dfrac{1}{x^{2}-16}<0\)

    Jibu

    \((-4,4)\)

    30. \(\dfrac{4}{x^{2}-25}>0\)

    31. \(\dfrac{4}{x-2} \geq \dfrac{3}{x+1}\)

    Jibu

    \([-10,-1) \cup(2, \infty)\)

    32. \(\dfrac{5}{x-1} \leq \dfrac{4}{x+2}\)

    Tatua Ukosefu wa usawa na Kazi za busara

    Katika mazoezi yafuatayo, tatua kila usawa wa kazi ya busara na uandike suluhisho katika maelezo ya muda.

    33. Kutokana na kazi\(R(x)=\dfrac{x-5}{x-2}\), kupata maadili ya\(x\) kwamba kufanya kazi chini ya au sawa na 0.

    Jibu

    \((2,5]\)

    34. Kutokana na kazi\(R(x)=\dfrac{x+1}{x+3}\), kupata maadili ya\(x\) kwamba kufanya kazi chini ya au sawa na 0.

    35. Kutokana na kazi\(R(x)=\dfrac{x-6}{x+2}\), kupata maadili ya\(x\) kwamba kufanya kazi chini ya au sawa na 0.

    Jibu

    \((-\infty,-2) \cup[6, \infty)\)

    36. Kutokana na kazi\(R(x)=\dfrac{x+1}{x-4}\), kupata maadili ya\(x\) kwamba kufanya kazi chini ya au sawa na 0.

    Mazoezi ya kuandika

    37. Andika hatua unazozitumia kuelezea kutatua usawa wa busara kwa ndugu yako mdogo.

    Jibu

    Majibu yatatofautiana

    38. Unda usawa wa busara ambao suluhisho ni\((-\infty,-2] \cup[4, \infty)\).