a, |x + 1/3| = 0

⇔ x + 1/3 = 0

⇔ x = -1/3

b, |x| - 3/5 = 5/9

⇔ |x| = 5/9 + 3/5

⇔ |x| = 52/45

⇔\(\left[ \begin{array}{l}x=52/45\\x=-52/45\end{array} \right.\) 

c, |x + 3/4| = 1/2

⇔ \(\left[ \begin{array}{l}x+3/4=1/2\\x+3/4=-1/2\end{array} \right.\) 

⇔ \(\left[ \begin{array}{l}x=-1/4\\x=-5/4\end{array} \right.\) 

d, |5/18 - x| - 7/24 = 0

⇔ |5/18 - x| = 7/24

⇔ \(\left[ \begin{array}{l}5/18-x=7/24\\5/18-x=-7/24\end{array} \right.\)

⇔ \(\left[ \begin{array}{l}x=-1/72\\x=41/72\end{array} \right.\)

e, 2/5 - |1/2 - x| = 6

⇔ |1/2 - x| = -28/5

Vì |1/2 - x| ≥ 0 nên  |1/2 - x| = -28/5 (vô lý)

⇒ Không có giá trị x thỏa mãn

f, |3/8 - x| + 5/6 = 7/4

⇔ |3/8 - x| = 11/12

⇔ \(\left[ \begin{array}{l}3/8-x=11/12\\3/8-x=-11/12\end{array} \right.\) 

⇔ \(\left[ \begin{array}{l}x=-13/24\\x=31/24\end{array} \right.\) 

g, |x : (-5/6) - 3/4| = 2

⇔ \(\left[ \begin{array}{l}x:(-5/6)-3/4=2\\x:(-5/6)-3/4=-2\end{array} \right.\) 

⇔\(\left[ \begin{array}{l}x:(-5/6)=11/4\\x:(-5/6)=-5/4\end{array} \right.\) 

⇔ \(\left[ \begin{array}{l}x=-55/24\\x=25/24\end{array} \right.\) 

h, |-2 : x + 5/6| = 3/4

⇔ \(\left[ \begin{array}{l}-2:x+5/6=3/4\\-2:x+5/6=-3/4\end{array} \right.\) 

⇔ \(\left[ \begin{array}{l}-2:x=-1/12\\-2:x=-19/12\end{array} \right.\) 

⇔ \(\left[ \begin{array}{l}x=24\\x=24/19\end{array} \right.\) 

i, |(-2/3)x + 3/8|(-8/5) = -8/15

⇔ |(-2/3)x + 3/8| = 1/3

⇔ \(\left[ \begin{array}{l}(-2/3)x+3/8=1/3\\(-2/3) x+3/8=-1/3\end{array} \right.\)

⇔  \(\left[ \begin{array}{l}(-2/3)x=-1/24\\(-2/3)x=-17/24\end{array} \right.\)

⇔ \(\left[ \begin{array}{l}x=1/16\\x=17/16\end{array} \right.\) 

k, |x + 1/2| + |y - 3/4| + |z -1| = 0

⇔ \(\left[ \begin{array}{l}|x+1/2|=0\\|y-3/4|=0\\|z-1|=0\end{array} \right.\) 

⇔ \(\left[ \begin{array}{l}x+1/2=0\\y-3/4=0\\z-1=0\end{array} \right.\) 

⇔ \(\left[ \begin{array}{l}x=-1/2\\y=3/4\\z=1\end{array} \right.\) 

 m, |x-3/4| + |2/5 - y| + |x-y+z| = 0

⇔ \(\left[ \begin{array}{l}|x-3/4|=0\\|2/5-y|=0\\|x-y+z|=0\end{array} \right.\) 

⇔ \(\left[ \begin{array}{l}x-3/4=0\\2/5-y=0\\x-y+z=0\end{array} \right.\) 

⇔ \(\left[ \begin{array}{l}x=3/4\\y=2/5\\z=-7/20\end{array} \right.\) 

n, |x-2/3| + |x+y+3/4| + |y-z-5/6| = 0

⇔ \(\left[ \begin{array}{l}|x-2/3|=0\\|x+y+3/4|=0\\|y-z-5/6|=0\end{array} \right.\) 

⇔ \(\left[ \begin{array}{l}x-2/3=0\\x+y+3/4=0\\y-z-5/6=0\end{array} \right.\) 

⇔ \(\left[ \begin{array}{l}x=2/3\\y=-17/12\\z=9/4\end{array} \right.\) 

Đáp án:

Giải thích các bước giải:

a) $|x+\frac{1}{3}|=0\\\Leftrightarrow x+\frac{1}{3}=0\\\Leftrightarrow x=-\frac{1}{3}$

b) $|x|-\frac{3}{5}=\frac{5}{9}\\\Leftrightarrow |x|=-\frac{2}{45}$

Suy ra, không có giá trị nào thão mãn cho x do gia strij tuyệt đối không bao giwof âm

c) $|x+\frac{3}{4}|=\frac{1}{2}\\TH1: x+\frac{3}{4}=\frac{1}{2}\\\Leftrightarrow x=-\frac{1}{4}\\TH2: x+\frac{3}{4}=-\frac{1}{2}\\\Leftrightarrow x=-\frac{5}{4}\\\Rightarrow x\in \{-\frac{1}{4}; -\frac{5}{4}\}$