次の計算をしなさい。 (1) $\frac{3x-2}{7} \times 21$ (2) $-15 \times \frac{2a+1}{3}$ (3) $7(x-3) + 6(-2x+5)$ (4) $3(2-5a) + 8(2a-4)$ (5) $3(4x+5) - 4(2x-3)$ (6) $-4(2a+6) - 5(-3a-5)$ (7) $4(\frac{1}{2}a + 2) + 9(\frac{2}{3}a - 1)$ (8) $\frac{1}{3}(6x-9) - \frac{2}{5}(5x+20)$

1. 問題の内容

次の計算をしなさい。

(1) $\frac{3x-2}{7} \times 21$

(2) $-15 \times \frac{2a+1}{3}$

(3) $7(x-3) + 6(-2x+5)$

(4) $3(2-5a) + 8(2a-4)$

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

(6) $-4(2a+6) - 5(-3a-5)$

(7) $4(\frac{1}{2}a + 2) + 9(\frac{2}{3}a - 1)$

(8) $\frac{1}{3}(6x-9) - \frac{2}{5}(5x+20)$

2. 解き方の手順

(1)

$\frac{3x-2}{7} \times 21 = (3x-2) \times 3 = 9x - 6$

(2)

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

(3)

$7(x-3) + 6(-2x+5) = 7x - 21 - 12x + 30 = -5x + 9$

(4)

$3(2-5a) + 8(2a-4) = 6 - 15a + 16a - 32 = a - 26$

(5)

$3(4x+5) - 4(2x-3) = 12x + 15 - 8x + 12 = 4x + 27$

(6)

$-4(2a+6) - 5(-3a-5) = -8a - 24 + 15a + 25 = 7a + 1$

(7)

$4(\frac{1}{2}a + 2) + 9(\frac{2}{3}a - 1) = 2a + 8 + 6a - 9 = 8a - 1$

(8)

$\frac{1}{3}(6x-9) - \frac{2}{5}(5x+20) = 2x - 3 - 2(x+4) = 2x - 3 - 2x - 8 = -11$

3. 最終的な答え

(1) $9x - 6$

(2) $-10a - 5$

(3) $-5x + 9$

(4) $a - 26$

(5) $4x + 27$

(6) $7a + 1$

(7) $8a - 1$

(8) $-11$