Pre-Algebra Examples

$\frac{3 x - 5}{x - 6} - \frac{9 x - 6}{x - 6} = \frac{1 - 6 x}{x - 6}$

Step 1

Simplify $\frac{3 x - 5}{x - 6} - \frac{9 x - 6}{x - 6}$ .

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Step 1.1

Combine the numerators over the common denominator.

$\frac{3 x - 5 - (9 x - 6)}{x - 6} = \frac{1 - 6 x}{x - 6}$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$\frac{3 x - 5 - (9 x) - - 6}{x - 6} = \frac{1 - 6 x}{x - 6}$

Step 1.2.2

Multiply $9$ by $- 1$ .

$\frac{3 x - 5 - 9 x - - 6}{x - 6} = \frac{1 - 6 x}{x - 6}$

Step 1.2.3

Multiply $- 1$ by $- 6$ .

$\frac{3 x - 5 - 9 x + 6}{x - 6} = \frac{1 - 6 x}{x - 6}$

Step 1.3

Simplify terms.

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Step 1.3.1

Subtract $9 x$ from $3 x$ .

$\frac{- 6 x - 5 + 6}{x - 6} = \frac{1 - 6 x}{x - 6}$

Step 1.3.2

Add $- 5$ and $6$ .

$\frac{- 6 x + 1}{x - 6} = \frac{1 - 6 x}{x - 6}$

Step 1.3.3

Factor $- 1$ out of $- 6 x$ .

$\frac{- (6 x) + 1}{x - 6} = \frac{1 - 6 x}{x - 6}$

Step 1.3.4

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{- (6 x) - 1 (- 1)}{x - 6} = \frac{1 - 6 x}{x - 6}$

Step 1.3.5

Factor $- 1$ out of $- (6 x) - 1 (- 1)$ .

$\frac{- (6 x - 1)}{x - 6} = \frac{1 - 6 x}{x - 6}$

Step 1.3.6

Simplify the expression.

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Step 1.3.6.1

Rewrite $- (6 x - 1)$ as $- 1 (6 x - 1)$ .

$\frac{- 1 (6 x - 1)}{x - 6} = \frac{1 - 6 x}{x - 6}$

Step 1.3.6.2

Move the negative in front of the fraction.

$- \frac{6 x - 1}{x - 6} = \frac{1 - 6 x}{x - 6}$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 49.8, - 49.7, - 49.5, - 49.4, - 49.2, - 49.1, - 49, - 48.9, - 48.7, - 48.6, - 48.5, - 48.3, - 48.2, - 48.1, - 48, - 47.9, - 47.8, - 47.7, - 47.5, - 47.4, - 47.3, - 47.1, - 47, - 46.9, - 46.8, - 46.6, - 46.5, - 46.2\overline{9}, - 46.1\overline{9}, - 46.0\overline{9}, - 46, - 45.6\overline{9}, - 45.4\overline{9}, - 45.3\overline{9}, - 45.2\overline{9}, - 45.1\overline{9}, - 45, - 44.8\overline{9}, - 44.7\overline{9}, - 44.5\overline{9}, - 44.4\overline{9}, - 44.3\overline{9}, - 44.2\overline{9}, - 44.1\overline{9}, - 44.0\overline{9}, - 43.8\overline{9}, - 43.7\overline{9}, - 43.6\overline{9}, - 43.5\overline{9}, - 43.4\overline{9}, - 43.3\overline{9}, - 43.2\overline{9}, - 43, - 42.8\overline{9}, - 42.2\overline{9}, - 42.0\overline{9}, - 41.8\overline{9}, - 41.6\overline{9}, - 41.5\overline{9}, - 41.3\overline{9}, - 41.2\overline{9}, - 41.1\overline{9}, - 41.0\overline{9}, - 40.8\overline{9}, - 40.6\overline{9}, - 40.4\overline{9}, - 40.3\overline{9}, - 40.1\overline{9}, - 40.0\overline{9}, - 39.8\overline{9}, - 39.6\overline{9}, - 39.5\overline{9}, - 39.4\overline{9}, - 39.3\overline{9}, - 39.2\overline{9}, - 39.1\overline{9}, - 38.8\overline{9}, - 38.7\overline{9}, - 38.6\overline{9}, - 38.4\overline{9}, - 38.3\overline{9}, - 38.2\overline{9}, - 38.1\overline{9}, - 38.0\overline{9}, - 37.6\overline{9}, - 37.5\overline{9}, - 37.4\overline{9}, - 37.3\overline{9}, - 37.1\overline{9}, - 37.0\overline{9}, - 36.7\overline{9}, - 36.5\overline{9}, - 36.4\overline{9}, - 36.3\overline{9}, - 36.2\overline{9}, - 36.1\overline{9}, - 36.0\overline{9}, - 36, - 35.8\overline{9}, - 35.7\overline{9}, - 35.6\overline{9}, - 35.5\overline{9}, - 35.3\overline{9}, - 35.2\overline{9}, - 35.1\overline{9}, - 35.0\overline{9}, - 35, - 34.8\overline{9}, - 34.7\overline{9}, - 34.6\overline{9}, - 34.5\overline{9}, - 34.4\overline{9}, - 34.2\overline{9}, - 34.1\overline{9}, - 34.0\overline{9}, - 33.8\overline{9}, - 33.7\overline{9}, - 33.6\overline{9}, - 33.5\overline{9}, - 33.3\overline{9}, - 33.2\overline{9}, - 33.1\overline{9}, - 33.0\overline{9}, - 33, - 32.8\overline{9}, - 32.6\overline{9}, - 32.3\overline{9}, - 32.1\overline{9}, - 32.0\overline{9}, - 32, - 31.7\overline{9}, - 31.6\overline{9}, - 31.5\overline{9}, - 31.4\overline{9}, - 31.3\overline{9}, - 31.2\overline{9}, - 31.0\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}, - 29.7\overline{9}, - 29.6\overline{9}, - 29.4\overline{9}, - 29.3\overline{9}, - 29.1\overline{9}, - 29.0\overline{9}, - 29, - 28.8\overline{9}, - 28.7\overline{9}, - 28.5\overline{9}, - 28.4\overline{9}, - 28.2\overline{9}, - 28.0\overline{9}, - 28, - 27.7\overline{9}, - 27.5\overline{9}, - 27.4\overline{9}, - 27.2\overline{9}, - 27.1\overline{9}, - 27.0\overline{9}, - 27, - 26.7\overline{9}, - 26.4\overline{9}, - 26.2\overline{9}, - 26.1\overline{9}, - 26, - 25.8\overline{9}, - 25.6\overline{9}, - 25.5\overline{9}, - 25.4\overline{9}, - 25.3\overline{9}, - 25.1\overline{9}, - 25.0\overline{9}, - 24.8\overline{9}, - 24.7\overline{9}, - 24.6\overline{9}, - 24.2\overline{9}, - 24.0\overline{9}, - 23.8\overline{9}, - 23.7\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}, - 22.4\overline{9}, - 22.3\overline{9}, - 22.2\overline{9}, - 22.1\overline{9}, - 21.8\overline{9}, - 21.7\overline{9}, - 21.4\overline{9}, - 21.3\overline{9}, - 21.0\overline{9}, - 20.8\overline{9}, - 20.7\overline{9}, - 20.4\overline{9}, - 20.1\overline{9}, - 20.0\overline{9}, - 20, - 19.8\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, - 18.8\overline{9}, - 18.6\overline{9}, - 18.5\overline{9}, - 18.3\overline{9}, - 18.2\overline{9}, - 18.0\overline{9}, - 18, - 17.7\overline{9}, - 17.6\overline{9}, - 17.3\overline{9}, - 17.2\overline{9}, - 17.0\overline{9}, - 17, - 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}, - 15.7\overline{9}, - 15.5\overline{9}, - 15.3\overline{9}, - 15.2\overline{9}, - 15.0\overline{9}, - 15, - 14.8\overline{9}, - 14.6\overline{9}, - 14.5\overline{9}, - \frac{29}{2}, - 14.3\overline{9}, - 14.2\overline{9}, - 14.1\overline{9}, - 14.0\overline{9}, - 13.6\overline{9}, - \frac{27}{2}, - 13.3\overline{9}, - 13.2\overline{9}, - 13.0\overline{9}, - 12.8\overline{9}, - 12.7\overline{9}, - 12.6\overline{9}, - 12.5\overline{9}, - \frac{62}{5}, - 12.1\overline{9}, - 12, - \frac{59}{5}, - 11.6\overline{9}, - \frac{23}{2}, - \frac{57}{5}, - 11.2\overline{9}, - 11.0\overline{9}, - 11, - 10.8\overline{9}, - \frac{54}{5}, - \frac{53}{5}, - \frac{52}{5}, - 10.2\overline{9}, - \frac{51}{5}, - 10, - \frac{49}{5}, - 9.7, - \frac{48}{5}, - \frac{19}{2}, - \frac{47}{5}, - 9.3, - \frac{46}{5}, - 9.1, - 9, - 8.9, - \frac{44}{5}, - \frac{17}{2}, - 8.3, - \frac{41}{5}, - 8.1, - 7.9, - \frac{39}{5}, - 7.7, - \frac{38}{5}, - \frac{15}{2}, - \frac{37}{5}, - \frac{36}{5}, - 7.1, - \frac{34}{5}, - 6.7, - \frac{13}{2}, - 6.3, - 6.1, - \frac{29}{5}, - 5.7, - \frac{11}{2}, - 5.3, - \frac{26}{5}, - 5.1, - 4.9, - 4.7, - \frac{22}{5}, - \frac{21}{5}, - 4, - 3.9, - \frac{19}{5}, - 3.7, - \frac{18}{5}, - \frac{16}{5}, - 3.1, - 2.9, - \frac{14}{5}, - \frac{13}{5}, - \frac{12}{5}, - \frac{11}{5}, - 2.1, - 2, - 1.9, - \frac{9}{5}, - 1.7, - \frac{8}{5}, - \frac{7}{5}, - 1.3, - \frac{6}{5}, - 1.1, - 1, - 0.9, - \frac{4}{5}, - 0.7, - \frac{3}{5}, - \frac{1}{2}, - \frac{2}{5}, - \frac{1}{5}, 0, 0.1, \frac{1}{5}, 0.3, \frac{1}{2}, \frac{3}{5}, 0.9, 1, 1.1, \frac{6}{5}, 1.3, \frac{3}{2}, \frac{8}{5}, 1.7, 2, \frac{11}{5}, \frac{12}{5}, \frac{5}{2}, \frac{13}{5}, 2.7, 2.9, 3, 3.1, \frac{16}{5}, 3.3, \frac{17}{5}, \frac{7}{2}, \frac{18}{5}, 3.7, \frac{19}{5}, 4, \frac{21}{5}, 4.3, \frac{9}{2}, \frac{23}{5}, \frac{24}{5}, 4.9, 5.1, \frac{26}{5}, \frac{27}{5}, \frac{28}{5}, 5.7, \frac{29}{5}, 5.9, 6.3, \frac{32}{5}, \frac{33}{5}, 6.7, \frac{34}{5}, 6.9, 7, 7.1, \frac{36}{5}, \frac{37}{5}, \frac{15}{2}, \frac{38}{5}, 7.7, \frac{39}{5}, 8, \frac{41}{5}, 8.3, \frac{42}{5}, \frac{43}{5}, 8.7, \frac{44}{5}, 9, 9.1, \frac{46}{5}, 9.3, \frac{47}{5}, \frac{19}{2}, \frac{48}{5}, \frac{49}{5}, 9.9, 10, 10.1, 10.3, \frac{52}{5}, \frac{21}{2}, \frac{53}{5}, \frac{54}{5}, 10.9, 11.1, \frac{56}{5}, 11.3, \frac{57}{5}, \frac{58}{5}, 11.7, \frac{59}{5}, 11.9, 12, 12.3, \frac{62}{5}, \frac{25}{2}, 12.6, 12.8, 12.9, 13, 13.1, 13.2, 13.3, \frac{27}{2}, 13.6, 13.7, 13.9, 14, 14.1, 14.4, 14.6, 14.7, 14.9, 15.2, 15.3, \frac{31}{2}, 15.6, 15.7, 15.8, 16, 16.3, 16.4, \frac{33}{2}, 16.7, 16.8, 16.9, 17.2, 17.3, 17.4, \frac{35}{2}, 18, 18.2, 18.3, 18.5, 18.7, 18.9, 19.1, 19.2, 19.4, 19.5, 19.6, 19.7, 20, 20.1, 20.3, 20.4, 20.6, 20.8, 20.9, 21.2, 21.3, 21.4, 21.5, 21.6, 21.7, 21.9, 22, 22.1, 22.2, 22.3, 22.5, 22.8, 23.1, 23.2, 23.3, 23.4, 23.5, 23.6, 23.7, 23.9, 24.1, 24.2, 24.4, 24.5, 24.6, 24.7, 24.8, 24.9, 25, 25.2, 25.5, 25.6, 25.9, 26.1, 26.3, 26.4, 26.5, 26.6, 26.7, 26.9, 27.1, 27.2, 27.4, 27.6, 27.8, 27.9, 28, 28.2, 28.3, 28.4, 28.5, 28.6, 28.7, 28.8, 28.9, 29, 29.1, 29.2, 29.4, 29.6, 29.7, 29.8, 29.9, 30.1, 30.4, 30.7, 30.8, 30.9, 31, 31.1, 31.2, 31.6, 31.7, 31.8, 31.9, 32.1, 32.2, 32.3, 32.5, 32.6, 32.7, 32.8, 33.1, 33.2, 33.4, 33.5, 33.7, 33.8, 33.9, 34.1, 34.2, 34.3, 34.4, 34.6, 34.7, 34.8, 35, 35.1, 35.4, 35.5, 35.7, 35.8, 36.1, 36.2, 36.3, 36.4, 36.6, 36.7, 36.9, 37, 37.1, 37.3, 37.4, 37.6, 37.7, 37.9, 38, 38.2, 38.3, 38.4, 38.5, 38.6, 38.7, 38.9, 39, 39.1, 39.2, 39.4, 39.5, 39.6, 39.8, 39.9, 40, 40.1, 40.5, 40.6, 40.7, 40.8, 40.9, 41.2, 41.3, 41.4, 41.5, 41.6, 41.7, 41.8, 41.9, 42, 42.2, 42.3, 42.4, 42.5, 42.6, 42.7, 42.8, 42.9, 43, 43.2, 43.3, 43.4, 43.5, 43.7, 43.8, 43.9, 44.2, 44.3, 44.4, 44.5, 44.6, 44.8, 44.9, 45, 45.1, 45.3, 45.4, 45.5, 45.6, 45.7, 45.8, 45.9, 46, 46.2, 46.3, 46.6, 46.7, 46.9, 47, 47.2, 47.4, 47.5, 47.6, 47.7, 47.8, 47.9, 48, 48.2, 48.4, 48.5, 48.6, 48.7, 48.8, 48.9, 49, 49.1, 49.2, 49.3, 49.4, 49.5, 49.7, 49.8, 49.9$

Step 3