与えられた数式を簡略化または解く問題です。 (11) $9-2a+8a$ (12) $-9+2a-8a$ (13) $-3a-5-2a$ (14) $(-9a)-(-8a)+3a$ (15) $-7x+4+2x-8$ (16) $-3x-2+5-4x$ (17) $-4-5x-1-3x$ (18) $\frac{x}{2}-3-\frac{2}{5}x+8$ (19) $-\frac{x}{3}-2+\frac{x}{4}-4$ (20) $-x+\frac{1}{4}+\frac{3}{7}x-\frac{5}{6}$

1. 問題の内容

与えられた数式を簡略化または解く問題です。

(11) $9-2a+8a$

(12) $-9+2a-8a$

(13) $-3a-5-2a$

(14) $(-9a)-(-8a)+3a$

(15) $-7x+4+2x-8$

(16) $-3x-2+5-4x$

(17) $-4-5x-1-3x$

(18) $\frac{x}{2}-3-\frac{2}{5}x+8$

(19) $-\frac{x}{3}-2+\frac{x}{4}-4$

(20) $-x+\frac{1}{4}+\frac{3}{7}x-\frac{5}{6}$

2. 解き方の手順

(11) $9-2a+8a = 9 + (-2+8)a = 9 + 6a = 6a + 9$

(12) $-9+2a-8a = -9 + (2-8)a = -9 - 6a = -6a - 9$

(13) $-3a-5-2a = (-3-2)a - 5 = -5a - 5$

(14) $(-9a)-(-8a)+3a = -9a + 8a + 3a = (-9+8+3)a = 2a$

(15) $-7x+4+2x-8 = (-7+2)x + (4-8) = -5x - 4$

(16) $-3x-2+5-4x = (-3-4)x + (-2+5) = -7x + 3$

(17) $-4-5x-1-3x = (-5-3)x + (-4-1) = -8x - 5$

(18) $\frac{x}{2}-3-\frac{2}{5}x+8 = (\frac{1}{2}-\frac{2}{5})x + (-3+8) = (\frac{5}{10}-\frac{4}{10})x + 5 = \frac{1}{10}x + 5$

(19) $-\frac{x}{3}-2+\frac{x}{4}-4 = (-\frac{1}{3}+\frac{1}{4})x + (-2-4) = (-\frac{4}{12}+\frac{3}{12})x - 6 = -\frac{1}{12}x - 6$

(20) $-x+\frac{1}{4}+\frac{3}{7}x-\frac{5}{6} = (-1+\frac{3}{7})x + (\frac{1}{4}-\frac{5}{6}) = (-\frac{7}{7}+\frac{3}{7})x + (\frac{3}{12}-\frac{10}{12}) = -\frac{4}{7}x - \frac{7}{12}$

3. 最終的な答え

(11) $6a + 9$

(12) $-6a - 9$

(13) $-5a - 5$

(14) $2a$

(15) $-5x - 4$

(16) $-7x + 3$

(17) $-8x - 5$

(18) $\frac{1}{10}x + 5$

(19) $-\frac{1}{12}x - 6$

(20) $-\frac{4}{7}x - \frac{7}{12}$