Розв’яжи рівняння:
Розв'язок:
1) $7(x - 2) = 5(x + 1)$
$7x - 14 = 5x + 5$
$7x - 5x = 5 + 14$
$2x = 19$
$x = \frac{19}{2} = 9\frac{1}{2}$;
2) $0{,}2 + 0{,}3(x - 9) = 5 - 1{,}7x$
$0{,}2 + 0{,}3x - 2{,}7 = 5 - 1{,}7x$
$-2{,}5 + 0{,}3x = 5 - 1{,}7x$
$0{,}3x + 1{,}7x = 5 + 2{,}5$
$2x = 7{,}5$
$x = 3{,}75$;
3) $|x| = 5$
$x = 5$ або $x = -5$;
4) $\frac{1}{2}(8 - x) = \frac{1}{3}(x + 1)$
$8 - x = \frac{2}{3}(x + 1)$
$8 - x = \frac{2}{3}x + \frac{2}{3}$
$24 - 3x = 2x + 2$
$-3x - 2x = 2 - 24$
$-5x = -22$
$x = \frac{22}{5} = 4\frac{2}{5}$;
5) $\frac{1}{3} - (x - 2) = \frac{1}{8}(x + 4)$
$\frac{1}{3} - x + 2 = \frac{1}{8}x + \frac{1}{2}$
$\frac{7}{3} - x = \frac{1}{8}x + \frac{1}{2}$
$56 - 24x = 3x + 12$
$-24x - 3x = 12 - 56$
$-27x = -44$
$x = \frac{44}{27} = 1\frac{17}{27}$;
6) $|x| = -7$
Розв’язку немає.