次の方程式を解きます。 (1) $x - 4 = 4(x + 2)$ (2) $5(x - 6) = 6 - x$ (3) $8 - 5(1 - x) = 13$ (4) $5x - 2(x - 3) = 15$ (5) $5x - 8(2x - 7) = 12$ (6) $5(x - 2) = 4(3x + 1)$

1. 問題の内容

次の方程式を解きます。

(1) $x - 4 = 4(x + 2)$

(2) $5(x - 6) = 6 - x$

(3) $8 - 5(1 - x) = 13$

(4) $5x - 2(x - 3) = 15$

(5) $5x - 8(2x - 7) = 12$

(6) $5(x - 2) = 4(3x + 1)$

2. 解き方の手順

(1)

$x - 4 = 4(x + 2)$

$x - 4 = 4x + 8$

$x - 4x = 8 + 4$

$-3x = 12$

$x = -4$

(2)

$5(x - 6) = 6 - x$

$5x - 30 = 6 - x$

$5x + x = 6 + 30$

$6x = 36$

$x = 6$

(3)

$8 - 5(1 - x) = 13$

$8 - 5 + 5x = 13$

$3 + 5x = 13$

$5x = 13 - 3$

$5x = 10$

$x = 2$

(4)

$5x - 2(x - 3) = 15$

$5x - 2x + 6 = 15$

$3x + 6 = 15$

$3x = 15 - 6$

$3x = 9$

$x = 3$

(5)

$5x - 8(2x - 7) = 12$

$5x - 16x + 56 = 12$

$-11x + 56 = 12$

$-11x = 12 - 56$

$-11x = -44$

$x = 4$

(6)

$5(x - 2) = 4(3x + 1)$

$5x - 10 = 12x + 4$

$5x - 12x = 4 + 10$

$-7x = 14$

$x = -2$

3. 最終的な答え

(1) $x = -4$

(2) $x = 6$

(3) $x = 2$

(4) $x = 3$

(5) $x = 4$

(6) $x = -2$