Giải thích các bước giải:
Bài 1:
1) $(-46)+(-35)-54-(-35)$
$=-46-35-54+35$
$=(-46-54)+(-35+35)$
$=-100$
2) $(-4).27.(-25)$
$=[(-4).(-25)].27$
$=100.27$
$=2700$
3) $(-4).125.(-25).(-6).(-8)$
$=[(-4).(-25)].[125.(-8)].6$
$=100.1000.6$
$=600000$
4) $(-34).25+25.(-66)$
$=25.(-34-66)$
$=25.(-100)$
$=-2500$
5) $254.(-27)+27.154$
$=254.(-27)+(-27).(-154)$
$=(-27).(254-154)$
$=(-27).100$
$=-2700$
6) $67.(-26)+26.(-33)$
$=67.(-26)+(-26).33$
$=(-26).(67+33)$
$=(-26).100$
$=-2600$
7) $(-68).(32+24)-32(24-68)$
$=(-68).32+(-68).24-32.24-32.(-68)$
$=[(-68).32-(-68).32]+[24.(-32-68)]$
$=24.(-100)$
$=-2400$
8) $(37-17).(-5)+23.(-13-17)$
$=20.(-5)+23.(-30)$
$=-100-690$
$=-790$
Bài 2:
1) $x-24=-58$
$⇒x=-58+24$
$⇒x=-34$
Vậy $x=-34$
2) $-36-x=-25$
$⇒-x=-25+36$
$⇒-x=11$
$⇒x=-11$
Vậy $x=-11$
3) $-54-(-x)=-27+(-13)$
$⇒-54+x=-27-13$
$⇒x=-27-13+54$
$⇒x=14$
Vậy $x=14$
4) $2x-(-34)=x-56$
$⇒2x+34=x-56$
$⇒2x-x=-56-34$
$⇒x=-90$
Vậy $x=-90$
5) $2(x-3)-17=x-(5-8)$
$⇒2x-6-17=x-(-3)$
$⇒2x-23=x+3$
$⇒2x-x=3+23$
$⇒x=26$
Vậy $x=26$
6) $3(x-2)=-2(x-5)-(-14)$
$⇒3x-6=-2x+10+14$
$⇒3x+2x=10+14+6$
$⇒5x=30$
$⇒x=6$
Vậy $x=6$
7) $-36+|x|=10$
$⇒|x|=10+36$
$⇒|x|=46$
$⇒x=±46$
Vậy $x∈\{-46;46\}$
8) $28-|x-1|=-12$
$⇒|x-1|=28+12$
$⇒|x-1|=40$
$⇒x-1=±40$
$⇒\left[ \begin{array}{l}x-1=40\\x-1=-40\end{array} \right.⇒\left[ \begin{array}{l}x=41\\x=-39\end{array} \right.$
Vậy $x∈\{-15;17\}$
9) $-14-|x-2|=-18$
$⇒|x-2|=18-14$
$⇒|x-2|=4$
$⇒x-2=±4$
$⇒\left[ \begin{array}{l}x-2=4\\x-2=-4\end{array} \right.⇒\left[ \begin{array}{l}x=6\\x=-2\end{array} \right.$
Vậy $x∈\{-2;6\}$
10) $(x-3)^3=-8$
$⇒(x-3)^3=(-2)^3$
$⇒x-3=-2$
$⇒x=1$
Vậy $x=1$
11) $12+(x-2)^2=21$
$⇒(x-2)^2=21-12$
$⇒(x-2)^2=9$
$⇒(x-2)^2=(±3)^2$
$⇒x-2=±3$
$⇒\left[ \begin{array}{l}x-2=3\\x-2=-3\end{array} \right.⇒\left[ \begin{array}{l}x=5\\x=-1\end{array} \right.$
Vậy $x∈\{-1;5\}$
