次の方程式を解きます。 (1) $1 - 0.2(2x+6) = 0$ (2) $0.8(3+x) = 1.6 - (1+x)$ (3) $\frac{1}{4}(2-x) + x = \frac{5}{6}$ (4) $\frac{x+4}{5} = \frac{4-x}{3}$ (5) $\frac{1}{2}x - \frac{x+1}{3} = -3$

1. 問題の内容

次の方程式を解きます。

(1) $1 - 0.2(2x+6) = 0$

(2) $0.8(3+x) = 1.6 - (1+x)$

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

(4) $\frac{x+4}{5} = \frac{4-x}{3}$

(5) $\frac{1}{2}x - \frac{x+1}{3} = -3$

2. 解き方の手順

(1) $1 - 0.2(2x+6) = 0$

$1 - 0.4x - 1.2 = 0$

$-0.4x = 0.2$

$x = \frac{0.2}{-0.4}$

$x = -\frac{1}{2}$

(2) $0.8(3+x) = 1.6 - (1+x)$

$2.4 + 0.8x = 1.6 - 1 - x$

$2.4 + 0.8x = 0.6 - x$

$0.8x + x = 0.6 - 2.4$

$1.8x = -1.8$

$x = \frac{-1.8}{1.8}$

$x = -1$

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

$\frac{1}{2} - \frac{x}{4} + x = \frac{5}{6}$

$-\frac{x}{4} + x = \frac{5}{6} - \frac{1}{2}$

$\frac{3}{4}x = \frac{5}{6} - \frac{3}{6}$

$\frac{3}{4}x = \frac{2}{6} = \frac{1}{3}$

$x = \frac{1}{3} \cdot \frac{4}{3}$

$x = \frac{4}{9}$

(4) $\frac{x+4}{5} = \frac{4-x}{3}$

両辺に$5 \times 3 = 15$をかける。

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

$3x + 12 = 20 - 5x$

$3x + 5x = 20 - 12$

$8x = 8$

$x = \frac{8}{8}$

$x = 1$

(5) $\frac{1}{2}x - \frac{x+1}{3} = -3$

両辺に$2 \times 3 = 6$をかける。

$3x - 2(x+1) = -18$

$3x - 2x - 2 = -18$

$x - 2 = -18$

$x = -18 + 2$

$x = -16$

3. 最終的な答え

(1) $x = -\frac{1}{2}$

(2) $x = -1$

(3) $x = \frac{4}{9}$

(4) $x = 1$

(5) $x = -16$