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Pertidaksamaan Nilai Mutlak, Irasional, dan Pecahan

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Pertidaksamaan Nilai Mutlak, Irasional, dan Pecahan

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Pertidaksamaan Nilai Mutlak, Irasional, dan Pecahan

  1. 1. Nama Kelompok :  Febriana Riska D.R. (18)  Helena Dwi Alex C. (19)  Irvan Afandy (21)  Nova Angelia E. (29)  Yuli Agustina (38)
  2. 2. Soal │ 3 − 2𝑥 ≤ 42 2+ 𝑥 𝟑−𝟐𝒙 │ 𝟐+𝒙 ≤ 𝟒 11 + 2𝑥 (3 − 2𝑥)2 ≤ 42 (2 + 𝑥)2 (3 − 2𝑥)2 ≤ 42 (2 + 𝑥)2 (3 − 2𝑥)2 − 42 (2 + 𝑥)2 ≤ 0 11 + 2𝑥 ≤ 0 2𝑥 ≤ −11 11 𝑥≤− 2 3 − 2𝑥 + 4 2 + 𝑥 3 − 2𝑥 − 4 2 + 𝑥 3 − 2𝑥 + 8 + 4𝑥 −5 − 6𝑥 ≤0 −5 − 6𝑥 ≤ 0 −5 ≤ 6𝑥 5 − ≤ 𝑥 6 ≤0 3 − 2𝑥 − 8 − 4𝑥 ≤ 0 𝐻𝑃 = {𝑥|𝑥 ≤ − 11 2 𝑎𝑡𝑎𝑢 − 5 6 ≤ 𝑥, 𝑥 ∈ 𝑅}
  3. 3. Soal |𝟑 + 3𝑥 + 7 𝑥 𝟕 | 𝒙 > 𝟏 4𝑥 + 7 2 > 12 (3𝑥 + 7)2 > 12 𝑥2 (3𝑥 + 7)2 > 12 (𝑥)2 (3𝑥 + 7)2 − 12 (𝑥)2 > 0 3𝑥 + 7 + 1(𝑥) 3𝑥 + 7 + 𝑥 4𝑥 + 7 > 0 4𝑥 > −7 𝑥 > −7 4 𝑥 > −1 3 4 3𝑥 + 7 − 𝑥 > 0 2𝑥 + 7 > 0 2𝑥 + 7 > 0 2𝑥 > −7 𝑥 > −7 2 𝑥 > −3 1 2 𝑥 < −3 1 2 3𝑥 + 7 − 1(𝑥) > 0 𝑯𝑷 𝒙 𝒙 < −𝟑 𝟏 𝟐 𝒂𝒕𝒂𝒖 𝒙 > −𝟏 𝟑 𝟒 , 𝒙 ∈ 𝑹
  4. 4. Soal 2− 𝑥−1 −2≥0 𝑥−1 −1 2− 𝑥+1 −2≥0 −𝑥 + 1 3− 𝑥 −2≥0 −𝑥 + 1 3 − 𝑥 + 2𝑥 − 2 ≥0 −𝑥 + 1 1+ 𝑥 ≥0 −𝑥 + 1 2− 𝑥−1  𝑥−1 −1 ≥2 1 + 𝑥 ≥ 0 𝑎𝑡𝑎𝑢 − 𝑥 + 1 ≥ 0 1≥ 𝑥 𝑥 ≥ −1 𝑥 > −1 𝐻𝑃 𝑥 −1 < 𝑥 ≤ 1, 𝑥 ∈ 𝑅
  5. 5. Soal 𝟓𝒙 − 𝟏 ≥ 𝟒 𝟐𝒙 + 𝟐 𝒔𝒚𝒂𝒓𝒂𝒕 ∶ 𝒙 ≠ −𝟏 5𝑥 − 1 −4≥0 2𝑥 + 2 5𝑥 − 1 − 8𝑥 − 8 ≥0 2𝑥 + 2 −3𝑥 − 9 ≥0 2𝑥 + 2 2𝑥 + 2 2𝑥 + 2 ≥ 0 2𝑥 ≥ −2 𝑥 ≥ −1 𝑥 > −1 −3 − 9 ≥ 0 atau −3𝑥 − 9 ≥ 0 −9 ≥ 3𝑥 −3 ≥ 𝑥 𝐻𝑃 𝑥 𝑥 ≤ −3 𝑎𝑡𝑎𝑢 𝑥 > −1, 𝑥 ∈ 𝑅
  6. 6.  Soal 3𝑥 − 2 𝑆𝑦𝑎𝑟𝑎𝑡 ∶ ≥0 4 3𝑥 − 2 ≥ 0.4 3𝑥 − 2 ≥ 0 3𝑥 ≥ 2 𝑥≥2 3 𝟑𝒙−𝟐 𝟒 ≤ 𝟐 3𝑥 − 2 ≤2 4 3𝑥 − 2 ≤4 4 3𝑥 − 2 ≤ 16 3𝑥 ≤ 18 𝑥≤6 𝐻𝑃 𝑥 2 3 ≤ 𝑥 ≤ 6, 𝑥 ∈ 𝑅
  7. 7.  3 − 5𝑥 ≤ 2 Soal 3 − 5𝑥 2 ≤ 22 9 − 5𝑥 ≤ 4 𝑠𝑦𝑎𝑟𝑎𝑡 ∶ 9 − 5𝑥 ≥ 0 9 ≥ 5𝑥 9 ≥ 𝑥 5 9 − 5𝑥 ≤ 4 9 − 5𝑥 ≤ 16 9 − 16 ≤ 5𝑥 −7 ≤ 5𝑥 −7 5 ≤ 𝑥 𝐻𝑃 𝑥 − 7 5 ≤ 𝑥 ≤ 9 5 , 𝑥 ∈ 𝑅

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