Đáp án:
Bài 2)
$1) x=-4\\
2) x=-2\\
3) x=43\\
4) {\left[\begin{aligned}x=5\\x=-1\end{aligned}\right.}\\
5) {\left[\begin{aligned}x=23\\x=-17\end{aligned}\right.}\\
6) {\left[\begin{aligned}x=20\\x=-22\end{aligned}\right.}\\
7) {\left[\begin{aligned}x=71\\x=-71\end{aligned}\right.}\\
8) {\left[\begin{aligned}x=5\\x=-3\end{aligned}\right.}$
Bài 3:
$a) \dfrac{44}{189}\\
b)\dfrac{-12}{23}\\
c)
\dfrac{-3}{7}\\
d)
\dfrac{1}{10}\\
e)\dfrac{3}{4}\\
g)
\dfrac{-2}{3}$
Bài 4:
$a) \dfrac{11}{26}\\
b)\dfrac{-967}{63}\\
c)-1\\
d)
0$
Giải thích các bước giải:
Bài 2)
$1) x-2=-6\Leftrightarrow x=-6+2=-4\\
2) -5x-(-3)=13\Leftrightarrow -5x=13-3=10\Leftrightarrow x=-2\\
3) 15-(x-7)=-21\Leftrightarrow x-7=15+21=36\Leftrightarrow x=36+7=43\\
4) \left | x-2 \right |=3\Leftrightarrow {\left[\begin{aligned}x-2=3\\x-2=-3\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=5\\x=-1\end{aligned}\right.}\\
5) \left | x-3 \right |-7=13\Leftrightarrow \left | x-3 \right |=13+7=20\\
\Leftrightarrow {\left[\begin{aligned}x-3=20\\x-3=-20\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=23\\x=-17\end{aligned}\right.}\\
6)72-3.\left | x+1 \right |=9\Leftrightarrow 3\left | x+1 \right |=72-9=63\\
\Leftrightarrow \left | x+1 \right |=21\\
\Leftrightarrow {\left[\begin{aligned}x+1=21\\x+1=-21\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=20\\x=-22\end{aligned}\right.}\\
7) 17-(43-|x|)=45\Leftrightarrow 43-|x|=17-45=-28\\
\Leftrightarrow |x|=43+28=71\\
\Leftrightarrow {\left[\begin{aligned}x=71\\x=-71\end{aligned}\right.}\\
8)3|x-1|-5=7\Leftrightarrow 3|x-1|=7+5=12\Leftrightarrow |x-1|=4\\
\Leftrightarrow {\left[\begin{aligned}x-1=4\\x-1=-4\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=5\\x=-3\end{aligned}\right.}$
Bài 3:
$a) \dfrac{1}{2}.\left ( \dfrac{2}{9}+\dfrac{3}{7}-\dfrac{5}{27} \right )\\
=\dfrac{1}{2}.\left ( \dfrac{42}{189}+\dfrac{81}{189}-\dfrac{35}{189} \right )
=\dfrac{1}{2}.\dfrac{88}{189}
=\dfrac{44}{189}\\
b)\left ( \dfrac{-5}{28}+1,75+\dfrac{8}{35} \right ):\left (-3\dfrac{9}{20} \right )
=\left ( \dfrac{-5}{28}+\dfrac{7}{4}+\dfrac{8}{35} \right ):\left (-3\dfrac{9}{20} \right )\\
=\left ( \dfrac{-25}{140}+\dfrac{245}{140}+\dfrac{32}{140} \right ):\left (\dfrac{-69}{20} \right )
=\dfrac{252}{140}.\dfrac{-20}{69}
=\dfrac{-12}{23}\\
c)
\dfrac{1}{3}.\dfrac{5}{7}-\dfrac{7}{27}.\dfrac{36}{14}\\
=\dfrac{1}{3}.\dfrac{5}{7}-\dfrac{7}{9.3}.\dfrac{9.4}{2.7}\\
=\dfrac{1}{3}.\dfrac{5}{7}-\dfrac{7}{3}.\dfrac{2}{7}
=\dfrac{1}{3.7}.(5-14)
=\dfrac{-9}{3.7}=\dfrac{-3}{7}\\
d)
70,5-528:\dfrac{15}{2}
=\dfrac{705}{10}-528.\dfrac{2}{15}
=\dfrac{141}{2}-\dfrac{352}{5}
=\dfrac{141.5}{10}-\dfrac{352.2}{10}
=\dfrac{1}{10}\\
e)\left ( \dfrac{3}{8}+\dfrac{-3}{4}+\dfrac{7}{12} \right ):\dfrac{5}{6}+\dfrac{1}{2}
=\left ( \dfrac{9}{24}+\dfrac{-18}{24}+\dfrac{14}{24} \right ).\dfrac{6}{5}+\dfrac{1}{2}
=\dfrac{5}{24}.\dfrac{6}{5}+\dfrac{1}{2}
=\dfrac{1}{4}+\dfrac{1}{2}
=\dfrac{1}{4}+\dfrac{2}{4}
=\dfrac{3}{4}\\
g)
\dfrac{\dfrac{2}{3}+\dfrac{2}{7}-\dfrac{1}{14}}{-1-\dfrac{3}{7}+\dfrac{3}{28}}\\
=\dfrac{\dfrac{28}{42}+\dfrac{12}{42}-\dfrac{3}{42}}{-\dfrac{28}{28}-\dfrac{12}{28}+\dfrac{3}{28}}\\
=\dfrac{\dfrac{37}{42}}{\dfrac{-37}{28}}
=\dfrac{37}{42}.\dfrac{-28}{37}
=\dfrac{-2}{3}$
Bài 4:
$a) \dfrac{-3}{7}+\dfrac{15}{26}-\left ( \dfrac{2}{13}-\dfrac{3}{7} \right )
=\dfrac{-3}{7}+\dfrac{15}{26}- \dfrac{2}{13}+\dfrac{3}{7}\\
=\left ( \dfrac{-3}{7}+\dfrac{3}{7} \right )+\left ( \dfrac{15}{26}- \dfrac{2}{13} \right )\\
=\dfrac{15}{26}- \dfrac{4}{26}
=\dfrac{11}{26}\\
b)2.\dfrac{3}{7}+\left ( \dfrac{2}{9}-1\dfrac{3}{7} \right )-\dfrac{5}{3}:\dfrac{1}{9}\\
=\dfrac{6}{7}+\dfrac{2}{9}-\dfrac{10}{7}-\dfrac{5}{3}.9
=\left (\dfrac{6}{7} -\dfrac{10}{7} \right )+\dfrac{2}{9}-15\\
=\dfrac{-4}{7}+\dfrac{2}{9}-15
=\dfrac{-36}{63}+\dfrac{14}{63}-\dfrac{945}{63}
=\dfrac{-967}{63}\\
c)\dfrac{-11}{23}.\dfrac{6}{7}+\dfrac{8}{7}.\dfrac{-11}{23}-\dfrac{1}{23}\\
=\dfrac{-11}{23}.\left ( \dfrac{6}{7}+\dfrac{8}{7} \right )-\dfrac{1}{23}\\
=\dfrac{-11}{23}.\dfrac{14}{7}-\dfrac{1}{23}
=\dfrac{-22}{23}-\dfrac{1}{23}
=\dfrac{-23}{23}=-1\\
d)
\left ( \dfrac{377}{-231}-\dfrac{123}{89}+\dfrac{34}{791} \right ).\left ( \dfrac{1}{6}-\dfrac{1}{8}-\dfrac{1}{24} \right )
=\left ( \dfrac{377}{-231}-\dfrac{123}{89}+\dfrac{34}{791} \right ).\left ( \dfrac{4}{24}-\dfrac{3}{24}-\dfrac{1}{24} \right )
=\left ( \dfrac{377}{-231}-\dfrac{123}{89}+\dfrac{34}{791} \right ).\dfrac{0}{24}
=0$
