$a = -3$ のとき、以下の式の値を求めよ。 (1) $-3a+4$ (2) $\frac{2a-3}{5}$ (3) $\frac{-5a+6}{8}$ (4) $-\frac{1}{6}(a-9)$ (5) $a^2$ (6) $2a^2$ (7) $-2a^2$ (8) $a^3$ (9) $-2a^3$ (10) $\frac{3a-1}{2} + \frac{2a+1}{3}$

1. 問題の内容

$a = -3$ のとき、以下の式の値を求めよ。

(1) $-3a+4$

(2) $\frac{2a-3}{5}$

(3) $\frac{-5a+6}{8}$

(4) $-\frac{1}{6}(a-9)$

(5) $a^2$

(6) $2a^2$

(7) $-2a^2$

(8) $a^3$

(9) $-2a^3$

(10) $\frac{3a-1}{2} + \frac{2a+1}{3}$

2. 解き方の手順

それぞれの式に $a = -3$ を代入して計算します。

(1) $-3a+4 = -3(-3)+4 = 9+4 = 13$

(2) $\frac{2a-3}{5} = \frac{2(-3)-3}{5} = \frac{-6-3}{5} = \frac{-9}{5} = -\frac{9}{5}$

(3) $\frac{-5a+6}{8} = \frac{-5(-3)+6}{8} = \frac{15+6}{8} = \frac{21}{8}$

(4) $-\frac{1}{6}(a-9) = -\frac{1}{6}(-3-9) = -\frac{1}{6}(-12) = \frac{12}{6} = 2$

(5) $a^2 = (-3)^2 = (-3)(-3) = 9$

(6) $2a^2 = 2(-3)^2 = 2(9) = 18$

(7) $-2a^2 = -2(-3)^2 = -2(9) = -18$

(8) $a^3 = (-3)^3 = (-3)(-3)(-3) = -27$

(9) $-2a^3 = -2(-3)^3 = -2(-27) = 54$

(10) $\frac{3a-1}{2} + \frac{2a+1}{3} = \frac{3(-3)-1}{2} + \frac{2(-3)+1}{3} = \frac{-9-1}{2} + \frac{-6+1}{3} = \frac{-10}{2} + \frac{-5}{3} = -5 - \frac{5}{3} = \frac{-15-5}{3} = \frac{-20}{3} = -\frac{20}{3}$

3. 最終的な答え

(1) 13

(2) $-\frac{9}{5}$

(3) $\frac{21}{8}$

(4) 2

(5) 9

(6) 18

(7) -18

(8) -27

(9) 54

(10) $-\frac{20}{3}$