Đại số sơ cấp Ví dụ

$2 x - 6 = 3 x + 1 - x - 7$

Bước 1

Rút gọn $3 x + 1 - x - 7$ .

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Bước 1.1

Trừ $x$ khỏi $3 x$ .

$2 x - 6 = 2 x + 1 - 7$

Bước 1.2

Trừ $7$ khỏi $1$ .

$2 x - 6 = 2 x - 6$

Bước 2

Vẽ đồ thị mỗi vế của phương trình. nghiệm là giá trị x của giao điểm.

$x \approx - 49.9, - 49.7, - 49.6, - 49.5, - 49.4, - 49.3, - 49.1, - 48.9, - 48.7, - 48.6, - 48.5, - 48.3, - 48.1, - 47.9, - 47.8, - 47.7, - 47.5, - 47.3, - 47.1, - 47, - 46.9, - 46.7, - 46.5, - 46.2\overline{9}, - 46.1\overline{9}, - 46.0\overline{9}, - 45.8\overline{9}, - 45.6\overline{9}, - 45.4\overline{9}, - 45.3\overline{9}, - 45.2\overline{9}, - 45.0\overline{9}, - 44.8\overline{9}, - 44.7\overline{9}, - 44.6\overline{9}, - 44.5\overline{9}, - 44.4\overline{9}, - 44.2\overline{9}, - 44.0\overline{9}, - 44, - 43.8\overline{9}, - 43.7\overline{9}, - 43.6\overline{9}, - 43.4\overline{9}, - 43.2\overline{9}, - 43.0\overline{9}, - 43, - 42.8\overline{9}, - 42.6\overline{9}, - 42.5\overline{9}, - 42.2\overline{9}, - 42.1\overline{9}, - 41.8\overline{9}, - 41.7\overline{9}, - 41.4\overline{9}, - 41.3\overline{9}, - 41.0\overline{9}, - 41, - 40.6\overline{9}, - 40.5\overline{9}, - 40.2\overline{9}, - 40.1\overline{9}, - 39.8\overline{9}, - 39.7\overline{9}, - 39.4\overline{9}, - 39.3\overline{9}, - 39.0\overline{9}, - 39, - 38.8\overline{9}, - 38.6\overline{9}, - 38.5\overline{9}, - 38.2\overline{9}, - 38.1\overline{9}, - 37.8\overline{9}, - 37.7\overline{9}, - 37.4\overline{9}, - 37.3\overline{9}, - 37.0\overline{9}, - 37, - 36.6\overline{9}, - 36.5\overline{9}, - 36.2\overline{9}, - 36.0\overline{9}, - 35.8\overline{9}, - 35.7\overline{9}, - 35.4\overline{9}, - 35.3\overline{9}, - 35.0\overline{9}, - 35, - 34.6\overline{9}, - 34.5\overline{9}, - 34.2\overline{9}, - 34.1\overline{9}, - 33.8\overline{9}, - 33.7\overline{9}, - 33.4\overline{9}, - 33.3\overline{9}, - 33.0\overline{9}, - 33, - 32.6\overline{9}, - 32.5\overline{9}, - 32.2\overline{9}, - 32.1\overline{9}, - 31.8\overline{9}, - 31.7\overline{9}, - 31.6\overline{9}, - 31.5\overline{9}, - 31.4\overline{9}, - 31.3\overline{9}, - 31.2\overline{9}, - 31.1\overline{9}, - 31.0\overline{9}, - 31, - 30.8\overline{9}, - 30.7\overline{9}, - 30.6\overline{9}, - 30.5\overline{9}, - 30.4\overline{9}, - 30.3\overline{9}, - 30.2\overline{9}, - 30.1\overline{9}, - 30.0\overline{9}, - 30, - 29.8\overline{9}, - 29.7\overline{9}, - 29.6\overline{9}, - 29.5\overline{9}, - 29.4\overline{9}, - 29.3\overline{9}, - 29.2\overline{9}, - 29.1\overline{9}, - 29.0\overline{9}, - 29, - 28.7\overline{9}, - 28.6\overline{9}, - 28.5\overline{9}, - 28.4\overline{9}, - 28.3\overline{9}, - 28.2\overline{9}, - 28.1\overline{9}, - 28.0\overline{9}, - 28, - 27.8\overline{9}, - 27.7\overline{9}, - 27.6\overline{9}, - 27.5\overline{9}, - 27.4\overline{9}, - 27.3\overline{9}, - 27.2\overline{9}, - 27.1\overline{9}, - 27.0\overline{9}, - 27, - 26.8\overline{9}, - 26.7\overline{9}, - 26.6\overline{9}, - 26.5\overline{9}, - 26.2\overline{9}, - 26.1\overline{9}, - 26, - 25.8\overline{9}, - 25.7\overline{9}, - 25.6\overline{9}, - 25.5\overline{9}, - 25.4\overline{9}, - 25.3\overline{9}, - 25.2\overline{9}, - 25.1\overline{9}, - 25.0\overline{9}, - 25, - 24.8\overline{9}, - 24.7\overline{9}, - 24.5\overline{9}, - 24.4\overline{9}, - 24.3\overline{9}, - 24.2\overline{9}, - 24.1\overline{9}, - 24.0\overline{9}, - 24, - 23.8\overline{9}, - 23.7\overline{9}, - 23.6\overline{9}, - 23.5\overline{9}, - 23.4\overline{9}, - 23.3\overline{9}, - 23.2\overline{9}, - 23.1\overline{9}, - 23.0\overline{9}, - 23, - 22.8\overline{9}, - 22.7\overline{9}, - 22.6\overline{9}, - 22.5\overline{9}, - 22.4\overline{9}, - 22.3\overline{9}, - 22.2\overline{9}, - 22.1\overline{9}, - 22.0\overline{9}, - 22, - 21.7\overline{9}, - 21.6\overline{9}, - 21.5\overline{9}, - 21.4\overline{9}, - 21.3\overline{9}, - 21.2\overline{9}, - 21.1\overline{9}, - 21.0\overline{9}, - 21, - 20.8\overline{9}, - 20.7\overline{9}, - 20.6\overline{9}, - 20.5\overline{9}, - 20.4\overline{9}, - 20.3\overline{9}, - 20.2\overline{9}, - 20.1\overline{9}, - 20.0\overline{9}, - 19.7\overline{9}, - 19.6\overline{9}, - 19.5\overline{9}, - 19.4\overline{9}, - 19.3\overline{9}, - 19.2\overline{9}, - 19.1\overline{9}, - 19.0\overline{9}, - 19, - 18.8\overline{9}, - 18.7\overline{9}, - 18.6\overline{9}, - 18.5\overline{9}, - 18.4\overline{9}, - 18.3\overline{9}, - 18.2\overline{9}, - 18.1\overline{9}, - 18.0\overline{9}, - 18, - 17.8\overline{9}, - 17.7\overline{9}, - 17.6\overline{9}, - 17.5\overline{9}, - \frac{35}{2}, - 17.3\overline{9}, - 17.2\overline{9}, - 17.1\overline{9}, - 17.0\overline{9}, - 17, - 16.8\overline{9}, - 16.7\overline{9}, - 16.6\overline{9}, - 16.5\overline{9}, - \frac{33}{2}, - 16.3\overline{9}, - 16.2\overline{9}, - 16.1\overline{9}, - 16.0\overline{9}, - 15.8\overline{9}, - 15.6\overline{9}, - 15.5\overline{9}, - 15.3\overline{9}, - 15.1\overline{9}, - 15.0\overline{9}, - 14.8\overline{9}, - 14.7\overline{9}, - 14.6\overline{9}, - 14.5\overline{9}, - \frac{29}{2}, - 14.2\overline{9}, - 14.1\overline{9}, - 14.0\overline{9}, - 14, - 13.7\overline{9}, - 13.6\overline{9}, - \frac{27}{2}, - 13.2\overline{9}, - 13.1\overline{9}, - 13, - 12.8\overline{9}, - 12.6\overline{9}, - 12.5\overline{9}, - \frac{25}{2}, - \frac{62}{5}, - 12.1\overline{9}, - 12.0\overline{9}, - 12, - 11.8\overline{9}, - \frac{59}{5}, - 11.6\overline{9}, - \frac{58}{5}, - \frac{23}{2}, - \frac{57}{5}, - 11.2\overline{9}, - 11.0\overline{9}, - 10.8\overline{9}, - \frac{54}{5}, - \frac{53}{5}, - \frac{21}{2}, - \frac{52}{5}, - 10.2\overline{9}, - 10.0\overline{9}, - 10, - 9.9, - \frac{49}{5}, - \frac{48}{5}, - \frac{19}{2}, - \frac{47}{5}, - 9.3, - 9.1, - 9, - 8.9, - \frac{44}{5}, - 8.7, - \frac{43}{5}, - \frac{17}{2}, - \frac{42}{5}, - 8.3, - \frac{41}{5}, - 8.1, - 8, - 7.9, - \frac{39}{5}, - 7.7, - \frac{38}{5}, - \frac{15}{2}, - \frac{37}{5}, - \frac{36}{5}, - 7.1, - 7, - 6.9, - \frac{34}{5}, - 6.7, - \frac{33}{5}, - \frac{13}{2}, - \frac{32}{5}, - 6.3, - \frac{31}{5}, - 6.1, - 6, - 5.9, - \frac{29}{5}, - 5.7, - \frac{28}{5}, - \frac{11}{2}, - \frac{27}{5}, - 5.3, - 4, - \frac{19}{5}, - 3.7, - \frac{18}{5}, - \frac{7}{2}, - \frac{17}{5}, - \frac{16}{5}, - 3, - 2.9, - \frac{14}{5}, - 2.7, - \frac{13}{5}, - \frac{12}{5}, - 2.3, - \frac{11}{5}, - 2, - 1.9, - \frac{9}{5}, - \frac{8}{5}, - \frac{3}{2}, - \frac{7}{5}, - \frac{6}{5}, - 1.1, - 0.9, - \frac{4}{5}, - \frac{3}{5}, - \frac{1}{2}, - 0.1, 0, 0.1, \frac{2}{5}, \frac{1}{2}, \frac{3}{5}, 0.9, 1, 1.1, 1.3, \frac{7}{5}, \frac{3}{2}, 1.7, 1.9, 2, 2.1, \frac{11}{5}, 2.3, \frac{5}{2}, \frac{13}{5}, \frac{14}{5}, \frac{16}{5}, 3.3, \frac{7}{2}, \frac{18}{5}, 4, \frac{11}{2}, \frac{28}{5}, 5.7, \frac{29}{5}, 5.9, 6, 6.1, \frac{31}{5}, 6.3, \frac{32}{5}, \frac{13}{2}, \frac{33}{5}, 6.7, \frac{34}{5}, 6.9, 7, 7.1, \frac{36}{5}, 7.3, \frac{37}{5}, \frac{15}{2}, \frac{38}{5}, 7.7, \frac{39}{5}, 7.9, 8, 8.1, \frac{41}{5}, 8.3, \frac{42}{5}, \frac{17}{2}, \frac{43}{5}, 8.7, \frac{44}{5}, 8.9, 9, 9.1, \frac{46}{5}, \frac{47}{5}, \frac{48}{5}, 9.7, \frac{49}{5}, 9.9, 10.1, \frac{51}{5}, 10.3, \frac{52}{5}, \frac{21}{2}, 10.7, 10.9, 11, 11.1, 11.3, \frac{57}{5}, \frac{23}{2}, \frac{59}{5}, 12, 12.3, \frac{25}{2}, 12.6, 12.8, 13, 13.1, 13.3, 13.4, 13.6, 13.8, 13.9, 14, 14.1, 14.2, 14.4, \frac{29}{2}, 14.6, 14.7, 14.9, 15, 15.2, 15.4, \frac{31}{2}, 15.7, 15.8, 16, 16.1, 16.2, 16.3, 16.4, \frac{33}{2}, 16.6, 16.7, 16.8, 16.9, 17, 17.1, 17.2, 17.3, 17.4, \frac{35}{2}, 17.6, 17.7, 17.8, 17.9, 18, 18.1, 18.2, 18.3, 18.4, 18.5, 18.6, 18.7, 18.8, 18.9, 19, 19.1, 19.2, 19.3, 19.4, 19.5, 19.6, 19.7, 19.8, 19.9, 20, 20.1, 20.2, 20.3, 20.4, 20.5, 20.6, 20.7, 20.8, 20.9, 21, 21.1, 21.2, 21.3, 21.5, 21.6, 21.9, 22, 22.1, 22.2, 22.3, 22.4, 22.5, 22.6, 22.7, 22.9, 23, 23.1, 23.2, 23.3, 23.4, 23.5, 23.6, 23.7, 23.8, 23.9, 24, 24.1, 24.3, 24.4, 24.7, 24.8, 24.9, 25, 25.1, 25.2, 25.3, 25.4, 25.5, 25.7, 25.8, 25.9, 26, 26.1, 26.2, 26.4, 26.5, 26.6, 26.7, 26.8, 26.9, 27.1, 27.2, 27.5, 27.6, 27.7, 27.8, 27.9, 28, 28.1, 28.2, 28.3, 28.4, 28.5, 28.6, 28.7, 28.8, 28.9, 29, 29.2, 29.3, 29.4, 29.5, 29.6, 29.7, 29.9, 30, 30.3, 30.4, 30.5, 30.6, 30.7, 30.8, 30.9, 31, 31.1, 31.2, 31.3, 31.4, 31.5, 31.6, 31.7, 31.8, 32.1, 32.2, 32.5, 32.6, 32.9, 33, 33.3, 33.4, 33.7, 33.8, 34.1, 34.2, 34.5, 34.6, 34.9, 35, 35.3, 35.4, 35.7, 35.8, 36.1, 36.2, 36.5, 36.6, 36.9, 37, 37.3, 37.4, 37.7, 37.8, 38.1, 38.2, 38.4, 38.6, 38.7, 38.8, 38.9, 39, 39.3, 39.4, 39.7, 39.8, 40.1, 40.2, 40.5, 40.6, 40.9, 41, 41.1, 41.2, 41.3, 41.4, 41.7, 41.8, 42.1, 42.2, 42.5, 42.6, 42.9, 43, 43.1, 43.3, 43.5, 43.7, 43.8, 43.9, 44, 44.3, 44.5, 44.6, 44.7, 44.9, 45.1, 45.3, 45.4, 45.5, 45.7, 45.9, 46.1, 46.2, 46.3, 46.5, 46.7, 46.8, 46.9, 47, 47.1, 47.3, 47.4, 47.7, 47.8, 47.9, 48.1, 48.3, 48.5, 48.6, 48.7, 48.9, 49.1, 49.3, 49.4, 49.5, 49.7, 49.9$

Bước 3