Bài $1$.
`407-{-512+[386+(407+512-386)]}`
`= 407 - {-512 + [386 + 407 + 512 - 386]}`
`= 407 - {-512 + 386 + 407 + 512 - 386}`
$= 407 + 512 - 386 - 407 - 512 + 386$
$= (407 - 407) + (512 - 512) + (-386+386)$
$= 0$
`-151+{-872-[361-(872+361+151)]}`
`= -151 + {-872 - [361 - 872 - 361 - 151]}`
`= -151 + {-872 - 361 + 872 + 361 + 151}`
`= -151 + {(-872+872)+(-361+361) + 151}`
$= -151 + 151$
$= 0$
Bài $2$.
$a$) $102 + 3.(x-71) = -12-39$
$⇔ 102 + 3.(x-71) = -51$
$⇔ 3(x-71) = -153$
$⇔ x - 71 = -51$
$⇔ x = 20$
Vậy $x=20$
$b$) $41-196:(2x-1)=25-33$
$⇔ 41 - 196:(2x-1) = -8$
$⇔ 196:(2x-1) = 49$
$⇔ 2x-1 = 4$
$⇔ x = \dfrac{5}{2}$ ($KTM$)
Vậy $x$ $∈$ $∅$
$c)57-2.|31-x|=13$
$⇔ 2.|31-x| = 44$
$⇔ |31-x| = 22$
$⇒$ \(\left[ \begin{array}{l}x=9\\x=53\end{array} \right.\)
Vậy $x$ $∈$ `{9;53}`
$d)13-7.(3x+1)^2=-162$
$⇔ 7.(3x+1)^2 = 175$
$⇔ (3x+1)^2 = 25$
$⇒$ $3x+1 = ±5$
$⇒$ \(\left[ \begin{array}{l}x=\dfrac{4}{3}(KTM)\\x=-2\end{array} \right.\)
Vậy $x=-2$
$e)-31-324:(x+1)^3=-19$
$⇔ 324 : (x+1)^3 = -12$
$⇔ (x+1)^3 = -27$
$⇔ x + 1 = -3$
$⇔ x = -4$
Vậy $x=-4$
Bài $3$.
$a$) $2x+81 \vdots x-1$
$⇔ 2x+81 - 2(x-1) \vdots x-1$
$⇔ 2x + 81 - 2x + 2 \vdots x-1$
$⇔ 83 \vdots x-1$
$⇒$ $x-1$ $∈$ `Ư(83)={±1;±83}`
$⇒$ $x$ $∈$ `{-82;0;2;84}`
Vậy $x$ $∈$ `{-82;0;2;84}`
$b$) $3x-36 \vdots x+1$
$⇔ 3x - 36 - 3(x+1) \vdots x+1$
$⇔ 3x - 36 - 3x - 3 \vdots x+1$
$⇔ -39 \vdots x+1$
$⇒$ $x+1$ $∈$ `Ư(39)={±1;±3;±13;±39}`
$⇒$ $x$ $∈$ `{-40;-14;-4;-2;0;2;12;38}`
Vậy $x$ $∈$ `{-40;-14;-4;-2;0;2;12;38}`
$c$) $5x-29 \vdots x-1$
$⇔ 5x-29 - 5(x-1) \vdots x-1$
$⇔ 5x-29 - 5x + 5 \vdots x-1$
$⇔ -24 \vdots x-1$
$⇒$ $x-1$ $∈$ `Ư(24)={±1;±2;±3;±4;±6;±8;±12;±24}`
$⇒$ $x$ $∈$ `{-23;-11;-7;-5;-3;-2;-1;0;2;3;4;5;7;9;13;25}`
Vậy $x$ $∈$ `{-23;-11;-7;-5;-3;-2;-1;0;2;3;4;5;7;9;13;25}`
