Bài 4:

a) $-\dfrac{1}{2}x+\dfrac{3}{4}=\dfrac{1}{3}-\dfrac{1}{2}$

$⇔-\dfrac{1}{2}x+\dfrac{3}{4}=\dfrac{2}{6}-\dfrac{3}{6}$

$⇔-\dfrac{1}{2}x+\dfrac{3}{4}=-\dfrac{1}{6}$

$⇔-\dfrac{1}{2}x=-\dfrac{1}{6}-\dfrac{3}{4}$

$⇔-\dfrac{1}{2}x=-\dfrac{2}{12}-\dfrac{9}{12}$

$⇔-\dfrac{1}{2}x=-\dfrac{11}{12}$

$⇔x=\dfrac{11}{12}:\dfrac{1}{2}$

$⇔x=\dfrac{11}{12}.2$

$⇔x=\dfrac{11}{6}$

b) $\Bigg|x+\dfrac{1}{5}\Bigg|=-2^2+5$

$⇔\Bigg|x+\dfrac{1}{5}\Bigg|=1$

$⇔\left[\begin{array}{l}x+\dfrac{1}{5}=1\\x+\dfrac{1}{5}=-1\end{array}\right.$

$⇔\left[\begin{array}{l}x=1-\dfrac{1}{5}\\x=-1-\dfrac{1}{5}\end{array}\right.$

$⇔\left[\begin{array}{l}x=\dfrac{4}{5}\\x=-\dfrac{6}{5}\end{array}\right.$

c) $-\dfrac{15}{12}x+\dfrac{3}{7}=\dfrac{6}{5}x-\dfrac{4}{7}$

$⇔-\dfrac{5}{4}x-\dfrac{6}{5}x=-\dfrac{3}{7}-\dfrac{4}{7}$

$⇔-\dfrac{25}{20}x-\dfrac{24}{20}x=-1$

$⇔-\dfrac{49}{20}x=-1$

$⇔x=1:\dfrac{49}{20}$

$⇔x=\dfrac{20}{49}$

d) $x\Bigg(x-\dfrac{1}{2}\Bigg)+\dfrac{3}{4}\Bigg(x-\dfrac{1}{2}\Bigg)=0$

$⇔\Bigg(x-\dfrac{1}{2}\Bigg)\Bigg(x+\dfrac{3}{4}\Bigg)=0$

$⇔\left[\begin{array}{l}x-\dfrac{1}{2}=0\\x+\dfrac{3}{4}=0\end{array}\right.$

$⇔\left[\begin{array}{l}x=\dfrac{1}{2}\\x=-\dfrac{3}{4}\end{array}\right.$

e) $(2x-1)^2=4^3$

$⇔(2x-1)^2=64$

$⇔(2x-1)^2=8^2$

$⇔\left[\begin{array}{l}2x-1=8\\2x-1=-8\end{array}\right.$

$⇔\left[\begin{array}{l}2x=9\\2x=-7\end{array}\right.$

$⇔\left[\begin{array}{l}x=\dfrac{9}{2}\\x=-\dfrac{7}{2}\end{array}\right.$

f) $|x-2|+|2-x|=4$

Với $x≥2 \to x-2≥0,\,2-x≤0$ ta có:

$x-2-(2-x)=4$

$⇔x-2-2+x=4$

$⇔2x=8$

$⇔x=4$ 

Với $x≤2 \to x-2≤0,\,2-x≥0$ ta có:

$-(x-2)+2-x=4$

$⇔-x+2+2-x=4$

$⇔-2x+4=4$

$⇔x=0$

Bài 5:

a) $-5\dfrac{1}{3}+2\dfrac{3}{4}<x<-2\dfrac{1}{6}.\dfrac{-13}{19}$

$\to -\dfrac{16}{3}+\dfrac{11}{4}<x<\dfrac{13}{6}.\dfrac{13}{19}$

$\to -\dfrac{31}{12}<x<\dfrac{169}{114}$

$\to x\in{\{-2;\,-1;\,0;\,1\}}$

b) $45\%-134\%<x<\Bigg(0,75-1\dfrac{1}{2}\Bigg).1\dfrac{5}{6}$

$\to \dfrac{9}{20}-\dfrac{67}{50}<x<-\dfrac{3}{4}.\dfrac{11}{6}$

$\to -\dfrac{89}{100}<x<-\dfrac{11}{8}$

$\to$ Không có số x thoả mãn

c) $\dfrac{1}{3}+\dfrac{3}{35}<\dfrac{x}{210}<\dfrac{4}{7}+\dfrac{3}{5}+\dfrac{1}{3}$

$\to \dfrac{44}{105}<\dfrac{x}{210}<\dfrac{158}{105}$

$\to \dfrac{88}{210}<\dfrac{x}{210}<\dfrac{316}{210}$

$\to 88<x<316$

$\to x\in{\{89,\,90,\,91,\,92,\,93,\,...,\,312,\,313,\,314,\,315\}}$

d) $4\dfrac{1}{3}\Bigg(\dfrac{1}{6}-\dfrac{1}{2}\Bigg)≤x≤\dfrac{2}{3}\Bigg(\dfrac{1}{3}-\dfrac{1}{2}-\dfrac{3}{4}\Bigg)$

$\to -\dfrac{13}{9}≤x≤-\dfrac{11}{18}$

$\to x=-1$