Pre-Algebra Examples

$\frac{1}{7} \cdot (14 r + 28) = 2 (r + 2)$

Step 1

Simplify $\frac{1}{7} \cdot (14 r + 28)$ .

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Step 1.1

Apply the distributive property.

$\frac{1}{7} (14 r) + \frac{1}{7} \cdot 28 = 2 (r + 2)$

Step 1.2

Cancel the common factor of $7$ .

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Step 1.2.1

Factor $7$ out of $14 r$ .

$\frac{1}{7} (7 (2 r)) + \frac{1}{7} \cdot 28 = 2 (r + 2)$

Step 1.2.2

Cancel the common factor.

$\frac{1}{7} (7 (2 r)) + \frac{1}{7} \cdot 28 = 2 (r + 2)$

Step 1.2.3

Rewrite the expression.

$2 r + \frac{1}{7} \cdot 28 = 2 (r + 2)$

Step 1.3

Cancel the common factor of $7$ .

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Step 1.3.1

Factor $7$ out of $28$ .

$2 r + \frac{1}{7} \cdot (7 (4)) = 2 (r + 2)$

Step 1.3.2

Cancel the common factor.

$2 r + \frac{1}{7} \cdot (7 \cdot 4) = 2 (r + 2)$

Step 1.3.3

Rewrite the expression.

$2 r + 4 = 2 (r + 2)$

Step 2

Simplify $2 (r + 2)$ .

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Step 2.1

Apply the distributive property.

$2 r + 4 = 2 r + 2 \cdot 2$

Step 2.2

Multiply $2$ by $2$ .

$2 r + 4 = 2 r + 4$

Step 3

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

$r \approx - 50, - 49.8, - 49.7, - 49.6, - 49.4, - 49.3, - 49.2, - 49, - 48.9, - 48.7, - 48.6, - 48.5, - 48.4, - 48.2, - 48.1, - 48, - 47.8, - 47.7, - 47.6, - 47.4, - 47.3, - 46.9, - 46.8, - 46.6, - 46.5, - 46.3\overline{9}, - 46.2\overline{9}, - 46.0\overline{9}, - 46, - 45.7\overline{9}, - 45.6\overline{9}, - 45.2\overline{9}, - 45.1\overline{9}, - 45, - 44.8\overline{9}, - 44.7\overline{9}, - 44.6\overline{9}, - 44.4\overline{9}, - 44.3\overline{9}, - 44.1\overline{9}, - 44.0\overline{9}, - 43.6\overline{9}, - 43.5\overline{9}, - 43.3\overline{9}, - 43.2\overline{9}, - 43.1\overline{9}, - 43.0\overline{9}, - 42.8\overline{9}, - 42.7\overline{9}, - 42.5\overline{9}, - 42.4\overline{9}, - 42.0\overline{9}, - 42, - 41.7\overline{9}, - 41.6\overline{9}, - 41.5\overline{9}, - 41.4\overline{9}, - 41, - 40.8\overline{9}, - 40.4\overline{9}, - 40.3\overline{9}, - 40.1\overline{9}, - 40.0\overline{9}, - 40, - 39.8\overline{9}, - 39.6\overline{9}, - 39.5\overline{9}, - 39.3\overline{9}, - 39.2\overline{9}, - 38.8\overline{9}, - 38.7\overline{9}, - 38.5\overline{9}, - 38.4\overline{9}, - 38.3\overline{9}, - 38.2\overline{9}, - 38.0\overline{9}, - 38, - 37.7\overline{9}, - 37.6\overline{9}, - 37.2\overline{9}, - 37.1\overline{9}, - 37, - 36.8\overline{9}, - 36.7\overline{9}, - 36.6\overline{9}, - 35.3\overline{9}, - 35.2\overline{9}, - 34.5\overline{9}, - 34.4\overline{9}, - 33.7\overline{9}, - 33.6\overline{9}, - 33, - 32.8\overline{9}, - 32.1\overline{9}, - 32.0\overline{9}, - 30.6\overline{9}, - 30.5\overline{9}, - 24.6\overline{9}, - 24.5\overline{9}, - 24.2\overline{9}, - 24.1\overline{9}, - 23.8\overline{9}, - 23.7\overline{9}, - 23.4\overline{9}, - 23.3\overline{9}, - 22.6\overline{9}, - 22.5\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}, - 21, - 20.6\overline{9}, - 20.5\overline{9}, - 20.2\overline{9}, - 20.1\overline{9}, - 19.8\overline{9}, - 19.7\overline{9}, - 19.4\overline{9}, - 19.3\overline{9}, - 19.0\overline{9}, - 19, - 18.6\overline{9}, - 18.5\overline{9}, - 18.2\overline{9}, - 18.1\overline{9}, - 15.8\overline{9}, - 15.7\overline{9}, - 15.3\overline{9}, - 15.2\overline{9}, - 15.0\overline{9}, - 15, - 14.5\overline{9}, - \frac{29}{2}, - 14.0\overline{9}, - 14, - 13.7\overline{9}, - 13.6\overline{9}, - \frac{27}{2}, - 13.3\overline{9}, - 12.6\overline{9}, - 12.5\overline{9}, - \frac{62}{5}, - 12.2\overline{9}, - 11.8\overline{9}, - \frac{59}{5}, - \frac{58}{5}, - \frac{23}{2}, - 11.0\overline{9}, - 11, - \frac{21}{2}, - \frac{52}{5}, - \frac{49}{5}, - 9.7, - \frac{19}{2}, - \frac{47}{5}, - 9, - 8.9, - 8.7, - \frac{17}{2}, - \frac{41}{5}, - 8.1, - 7.9, - 7.7, - \frac{37}{5}, - 7.3, - 7.1, - 6.9, - \frac{33}{5}, - \frac{13}{2}, - 6.3, - 6.1, - 5.9, - \frac{29}{5}, - 5.7, - \frac{11}{2}, - \frac{26}{5}, - 5.1, - 5, - 4.9, - 4.7, - \frac{9}{2}, - \frac{21}{5}, - 4.1, - 3.7, - \frac{18}{5}, - \frac{16}{5}, - 3.1, - 2.9, - \frac{14}{5}, - 2.7, - \frac{13}{5}, - \frac{5}{2}, - \frac{12}{5}, - 2.3, - \frac{11}{5}, - 2.1, - 1.9, - 1.7, - \frac{8}{5}, - \frac{7}{5}, - 1.3, - 1.1, - 1, - 0.9, - \frac{4}{5}, - \frac{3}{5}, - \frac{2}{5}, - 0.3, - \frac{1}{5}, - 0.1, 0, \frac{2}{5}, \frac{1}{2}, 0.7, \frac{4}{5}, 0.9, 1, 1.1, \frac{6}{5}, 1.3, \frac{7}{5}, \frac{3}{2}, \frac{8}{5}, 1.7, \frac{9}{5}, 1.9, 2, \frac{11}{5}, 2.3, \frac{12}{5}, \frac{13}{5}, \frac{14}{5}, 2.9, 3, \frac{16}{5}, \frac{7}{2}, \frac{18}{5}, \frac{19}{5}, 4, 4.1, 4.3, \frac{9}{2}, \frac{23}{5}, 4.7, \frac{24}{5}, 4.9, 5.1, 5.3, \frac{27}{5}, \frac{11}{2}, \frac{28}{5}, 5.7, 5.9, 6.1, \frac{33}{5}, 6.7, \frac{34}{5}, 6.9, \frac{37}{5}, \frac{15}{2}, 7.7, \frac{39}{5}, 7.9, 8.1, \frac{41}{5}, 8.3, \frac{42}{5}, \frac{17}{2}, 8.7, \frac{44}{5}, 9, 9.1, 9.3, \frac{19}{2}, \frac{48}{5}, 9.7, \frac{49}{5}, 9.9, 10, 10.1, \frac{51}{5}, 10.3, \frac{52}{5}, \frac{21}{2}, \frac{53}{5}, 10.7, \frac{54}{5}, 10.9, 11, 11.1, \frac{56}{5}, 11.3, \frac{57}{5}, \frac{23}{2}, \frac{58}{5}, 11.7, \frac{59}{5}, 11.9, 12, 12.1, 12.2, 12.3, \frac{62}{5}, \frac{25}{2}, 12.6, 12.8, 12.9, 13, 13.1, 13.2, 13.3, 13.4, \frac{27}{2}, 13.6, 13.7, 13.8, 13.9, 14.1, 14.2, 14.4, \frac{29}{2}, 14.6, 14.7, 14.8, 14.9, 15, 15.2, 15.3, 15.4, \frac{31}{2}, 15.7, 15.8, 16, 16.3, 16.4, \frac{33}{2}, 16.6, 16.7, 16.8, 17, 17.1, 17.2, 17.3, 17.4, \frac{35}{2}, 17.6, 17.8, 17.9, 18, 18.1, 18.2, 18.3, 18.4, 18.6, 18.7, 18.8, 19, 19.1, 19.2, 19.4, 19.5, 19.6, 19.8, 19.9, 20, 20.2, 20.3, 20.6, 20.7, 20.8, 21, 21.2, 21.4, 21.6, 21.8, 22, 22.2, 22.4, 22.5, 22.8, 23, 23.2, 23.4, 23.6, 23.8, 24, 24.2, 24.4, 24.6, 24.8, 25, 25.2, 25.4, 25.6, 25.8, 25.9, 26, 26.2, 26.4, 26.6, 26.8, 27, 27.2, 27.4, 27.6, 27.8, 28, 28.2, 28.4, 28.6, 28.7, 28.8, 29.1, 29.2, 29.4, 29.6, 29.7, 29.8, 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, 32, 32.2, 32.3, 32.6, 32.7, 33, 33.1, 33.4, 33.5, 33.8, 33.9, 34.2, 34.3, 34.6, 34.7, 34.9, 35, 35.1, 35.2, 35.3, 35.4, 35.6, 35.7, 35.8, 36, 36.2, 36.3, 36.5, 36.6, 36.7, 36.8, 36.9, 37, 37.1, 37.2, 37.3, 37.4, 37.5, 37.7, 37.8, 37.9, 38.1, 38.2, 38.3, 38.4, 38.5, 38.6, 38.7, 38.8, 38.9, 39, 39.1, 39.3, 39.4, 39.5, 39.7, 39.8, 39.9, 40, 40.1, 40.2, 40.3, 40.4, 40.5, 40.6, 40.7, 40.9, 41, 41.1, 41.3, 41.4, 41.5, 41.6, 41.7, 41.8, 41.9, 42, 42.1, 42.2, 42.3, 42.5, 42.6, 42.7, 42.9, 43, 43.1, 43.2, 43.3, 43.4, 43.5, 43.6, 43.7, 43.8, 43.9, 44, 44.1, 44.2, 44.3, 44.4, 44.5, 44.6, 44.7, 44.9, 45, 45.1, 45.3, 45.4, 45.5, 45.6, 45.7, 45.8, 45.9, 46, 46.1, 46.2, 46.3, 46.5, 46.6, 46.7, 46.8, 46.9, 47, 47.1, 47.2, 47.3, 47.4, 47.5, 47.6, 47.7, 47.8, 47.9, 48.1, 48.2, 48.3, 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 4