Giải câu 2 trang 15 sách toán VNEN lớp 8 tập 2.
a) $\frac{3x-2}{2}$ = $\frac{1-2x}{3}$
* Ta có: $\frac{3x-2}{2}$ = $\frac{1-2x}{3}$
$\Leftrightarrow $ $\frac{(9x-6}{6}$ = $\frac{2-4x}{6}$
$\Leftrightarrow $ 9x - 6 = 2 - 4x
$\Leftrightarrow $ 9x + 4x = 2 + 6
$\Leftrightarrow $ 13x = 8
$\Leftrightarrow $ x = $\frac{8}{13}$
b) Ta có: $\frac{x-1}{3}$ + 2 = 3 - $\frac{2x + 5}{4}$
$\Leftrightarrow $ $\frac{x - 1 + 6}{3}$ = $\frac{12 - 2x - 5}{4}$
$\Leftrightarrow $ $\frac{4x - 4 + 24}{12}$ = $\frac{36 - 6x - 15}{12}$
$\Leftrightarrow $ 4x - 4 + 24 = 36 - 6x - 15
$\Leftrightarrow $ 4x + 6x = 36 - 15 - 24 + 4
$\Leftrightarrow $ 10x = 1
$\Leftrightarrow $ x = $\frac{1}{10}$
c) Ta có: $\frac{x - 1}{5}$ + x = $\frac{x+1}{7}$
$\Leftrightarrow $ $\frac{x - 1 + 5x}{5}$ = $\frac{x+1}{7}$
$\Leftrightarrow $ $\frac{7x - 7 + 35x}{35}$ = $\frac{5x+5}{35}$
$\Leftrightarrow $ 7x - 7 + 35x = 5x + 5
$\Leftrightarrow $ 7x + 35x - 5x = 5 +7
$\Leftrightarrow $ 37x = 12
$\Leftrightarrow $ x = $\frac{12}{37}$
d) Ta có: 2(x - 2,5) = 0,25 + $\frac{4x - 3}{8}$
$\Leftrightarrow $ $\frac{16x - 40}{8}$ = $\frac{2 + 4x - 3}{8}$
$\Leftrightarrow $ 16x - 40 = 2 + 4x - 3
$\Leftrightarrow $ 16x - 4x = 2 - 3 + 40
$\Leftrightarrow $ 12x = 39
$\Leftrightarrow $ x = $\frac{39}{12}$