解下列方程:
(1)$5(3-2x)-12(5-2x)= 11$; (2)$\frac {3}{4}[\frac {4}{3}(\frac {1}{2}t-\frac {1}{4})-8]= \frac {3}{2}t-1$;
(3)$2-\frac {x-5}{6}= x-\frac {x+1}{3}$; (4)$x-\frac {1-x}{3}= 1$;
(5)$\frac {0.1x+0.1}{0.3}-\frac {0.3x-0.5}{0.4}= 1$; (6)$\frac {x-3}{0.15}-\frac {x+4}{0.2}= -10$;
(7)$\frac {3+0.2x}{0.2}-\frac {0.2+0.03x}{0.01}= 0.75$; (8)$\frac {x-2}{3}-0.5= \frac {5x}{6}$.
(1)$5(3-2x)-12(5-2x)= 11$; (2)$\frac {3}{4}[\frac {4}{3}(\frac {1}{2}t-\frac {1}{4})-8]= \frac {3}{2}t-1$;
(3)$2-\frac {x-5}{6}= x-\frac {x+1}{3}$; (4)$x-\frac {1-x}{3}= 1$;
(5)$\frac {0.1x+0.1}{0.3}-\frac {0.3x-0.5}{0.4}= 1$; (6)$\frac {x-3}{0.15}-\frac {x+4}{0.2}= -10$;
(7)$\frac {3+0.2x}{0.2}-\frac {0.2+0.03x}{0.01}= 0.75$; (8)$\frac {x-2}{3}-0.5= \frac {5x}{6}$.
答案:(1)$x=4$ (2)$t=-\frac{21}{4}$ (3)$x=\frac{19}{5}$ (4)$x=1$ (5)$x=\frac{7}{5}$ (6)$x=18$ (7)$x=-\frac{23}{8}$ (8)$x=-\frac{7}{3}$
解析:
(1)解:$5(3 - 2x) - 12(5 - 2x) = 11$
$15 - 10x - 60 + 24x = 11$
$14x - 45 = 11$
$14x = 56$
$x = 4$
(2)解:$\frac{3}{4}\left[\frac{4}{3}\left(\frac{1}{2}t - \frac{1}{4}\right)-8\right]=\frac{3}{2}t - 1$
$\left(\frac{1}{2}t - \frac{1}{4}\right)-6=\frac{3}{2}t - 1$
$\frac{1}{2}t - \frac{1}{4}-6=\frac{3}{2}t - 1$
$-\frac{1}{2}t - \frac{25}{4}=-1$
$-\frac{1}{2}t=\frac{21}{4}$
$t=-\frac{21}{4}$
(3)解:$2 - \frac{x - 5}{6}=x - \frac{x + 1}{3}$
$12 - (x - 5)=6x - 2(x + 1)$
$12 - x + 5=6x - 2x - 2$
$17 - x=4x - 2$
$-5x=-19$
$x=\frac{19}{5}$
(4)解:$x - \frac{1 - x}{3}=1$
$3x-(1 - x)=3$
$3x - 1 + x=3$
$4x=4$
$x = 1$
(5)解:$\frac{0.1x + 0.1}{0.3}-\frac{0.3x - 0.5}{0.4}=1$
$\frac{x + 1}{3}-\frac{3x - 5}{4}=1$
$4(x + 1)-3(3x - 5)=12$
$4x + 4 - 9x + 15=12$
$-5x + 19=12$
$-5x=-7$
$x=\frac{7}{5}$
(6)解:$\frac{x - 3}{0.15}-\frac{x + 4}{0.2}=-10$
$\frac{100x - 300}{15}-\frac{10x + 40}{2}=-10$
$\frac{20x - 60}{3}-(5x + 20)=-10$
$\frac{20x - 60}{3}-5x - 20=-10$
$20x - 60 - 15x - 60=-30$
$5x - 120=-30$
$5x=90$
$x = 18$
(7)解:$\frac{3 + 0.2x}{0.2}-\frac{0.2 + 0.03x}{0.01}=0.75$
$\frac{30 + 2x}{2}-(20 + 3x)=0.75$
$15 + x - 20 - 3x=0.75$
$-2x - 5=0.75$
$-2x=5.75$
$x=-\frac{23}{8}$
(8)解:$\frac{x - 2}{3}-0.5=\frac{5x}{6}$
$2(x - 2)-3=5x$
$2x - 4 - 3=5x$
$-3x=7$
$x=-\frac{7}{3}$
$15 - 10x - 60 + 24x = 11$
$14x - 45 = 11$
$14x = 56$
$x = 4$
(2)解:$\frac{3}{4}\left[\frac{4}{3}\left(\frac{1}{2}t - \frac{1}{4}\right)-8\right]=\frac{3}{2}t - 1$
$\left(\frac{1}{2}t - \frac{1}{4}\right)-6=\frac{3}{2}t - 1$
$\frac{1}{2}t - \frac{1}{4}-6=\frac{3}{2}t - 1$
$-\frac{1}{2}t - \frac{25}{4}=-1$
$-\frac{1}{2}t=\frac{21}{4}$
$t=-\frac{21}{4}$
(3)解:$2 - \frac{x - 5}{6}=x - \frac{x + 1}{3}$
$12 - (x - 5)=6x - 2(x + 1)$
$12 - x + 5=6x - 2x - 2$
$17 - x=4x - 2$
$-5x=-19$
$x=\frac{19}{5}$
(4)解:$x - \frac{1 - x}{3}=1$
$3x-(1 - x)=3$
$3x - 1 + x=3$
$4x=4$
$x = 1$
(5)解:$\frac{0.1x + 0.1}{0.3}-\frac{0.3x - 0.5}{0.4}=1$
$\frac{x + 1}{3}-\frac{3x - 5}{4}=1$
$4(x + 1)-3(3x - 5)=12$
$4x + 4 - 9x + 15=12$
$-5x + 19=12$
$-5x=-7$
$x=\frac{7}{5}$
(6)解:$\frac{x - 3}{0.15}-\frac{x + 4}{0.2}=-10$
$\frac{100x - 300}{15}-\frac{10x + 40}{2}=-10$
$\frac{20x - 60}{3}-(5x + 20)=-10$
$\frac{20x - 60}{3}-5x - 20=-10$
$20x - 60 - 15x - 60=-30$
$5x - 120=-30$
$5x=90$
$x = 18$
(7)解:$\frac{3 + 0.2x}{0.2}-\frac{0.2 + 0.03x}{0.01}=0.75$
$\frac{30 + 2x}{2}-(20 + 3x)=0.75$
$15 + x - 20 - 3x=0.75$
$-2x - 5=0.75$
$-2x=5.75$
$x=-\frac{23}{8}$
(8)解:$\frac{x - 2}{3}-0.5=\frac{5x}{6}$
$2(x - 2)-3=5x$
$2x - 4 - 3=5x$
$-3x=7$
$x=-\frac{7}{3}$