Đáp án:
$2)
a) x=\pm \dfrac{23}{8}\\
b)
x=\dfrac{19}{30}\\
c)
x=\pm \dfrac{13}{27}\\
d)
x=\dfrac{13}{4}\\
e) {\left[\begin{aligned}x=\dfrac{7}{10}\\ x=-\dfrac{11}{10}\end{aligned}\right.}\\
f)
{\left[\begin{aligned}x=\dfrac{-1}{10}\\x=\dfrac{5}{10}=\dfrac{1}{2}\end{aligned}\right.}\\
3)
a)1\\
b)\dfrac{-4}{3}\\
c) -10\\
d) -9\\
e) -2$
Giải thích các bước giải:
$2)
a) |x|-\dfrac{5}{2}=\dfrac{3}{8}\\
\Leftrightarrow |x|=\dfrac{3}{8}+\dfrac{5}{2}\\
\Leftrightarrow |x|=\dfrac{3}{8}+\dfrac{20}{8}\\
\Leftrightarrow x=\pm \dfrac{23}{8}\\
b)
\left | -\dfrac{1}{6} \right |+x=\left | -\dfrac{4}{5} \right |\\
\Leftrightarrow x=\dfrac{4}{5}-\dfrac{1}{6}\\
\Leftrightarrow x=\dfrac{24}{30}-\dfrac{5}{30}\\
\Leftrightarrow x=\dfrac{19}{30}\\
c)
\dfrac{4}{9}-|x|=\dfrac{-1}{27}\\
\Leftrightarrow -|x|=\dfrac{-1}{27}-\dfrac{4}{9}\\
\Leftrightarrow -|x|=\dfrac{-1}{27}-\dfrac{12}{27}\\
\Leftrightarrow -|x|=\dfrac{-13}{27}\\
\Leftrightarrow |x|=\dfrac{13}{27}\\
\Leftrightarrow x=\pm \dfrac{13}{27}\\
d)
\left | \dfrac{3}{2} \right |-x=-\left |\dfrac{-7}{4} \right |\\
\Leftrightarrow x=\dfrac{3}{2}+\dfrac{7}{4}\\
\Leftrightarrow x=\dfrac{6}{4}+\dfrac{7}{4}\\
\Leftrightarrow x=\dfrac{13}{4}\\
e) \left | x+\dfrac{1}{5} \right |=\dfrac{9}{10}\\
\Leftrightarrow {\left[\begin{aligned}x+\dfrac{1}{5}=\dfrac{9}{10}\\ x+\dfrac{1}{5}=-\dfrac{9}{10}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{9}{10}-\dfrac{1}{5}\\ x=-\dfrac{9}{10}-\dfrac{1}{5}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{9}{10}-\dfrac{2}{10}\\ x=-\dfrac{9}{10}-\dfrac{2}{10}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{7}{10}\\ x=-\dfrac{11}{10}\end{aligned}\right.}\\
f)
\left | \dfrac{1}{5}-x \right |=\left | -\dfrac{3}{10} \right |\\
\Leftrightarrow {\left[\begin{aligned}\dfrac{1}{5}-x=\dfrac{3}{10}\\\dfrac{1}{5}-x=-\dfrac{3}{10}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{2}{10}-\dfrac{3}{10}\\x=\dfrac{2}{10}+\dfrac{3}{10}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{-1}{10}\\x=\dfrac{5}{10}=\dfrac{1}{2}\end{aligned}\right.}\\
3)
a)|-2,5|-|-1,5|+|0|=2,5-1,5+0=1\\
b) |-0,75|-2\dfrac{1}{3}+\dfrac{1}{4}=\dfrac{3}{4}-\dfrac{7}{3}+\dfrac{1}{4}\\
=\left ( \dfrac{3}{4}+\dfrac{1}{4} \right )-\dfrac{7}{3}\\
=1-\dfrac{7}{3}=\dfrac{3}{3}-\dfrac{7}{3}=\dfrac{-4}{3}\\
c) (-16).\left | -\dfrac{1}{2}-\dfrac{1}{4} \right |-(-2)\\
=(-16).\left | -\dfrac{2}{4}-\dfrac{1}{4} \right |+2\\
=(-16).\dfrac{3}{4}+2\\
=-12+2=-10\\
d) |-25|:(-5)+(-4)=25:(-5)+(-4)=-5+(-4)=-9\\
e) |20|-|18|+|+6|-|+10|-|0|=20-18+6-10-0=-2$
