Question

a) 3 - | x + 7| - \(\frac{1}{2}\)= \(\frac{1}{3}\)

b)  | x- 1,5 | + | x - 2,5 | = 0

c) 1,7 + | 3,4 - x | = 6

d) 5 . | x - 28 | -3,5 = \(\frac{1}{2}\)

e) | x- \(\frac{1}{2}\)| . (x + 1) = 0

nhanh mình dang gấp

Answer 1

a.3 - | x + 7 | - 1/2 = 1/3

3 - | x + 7 | = 1/3 +1/2

3 - | x +7 | = 5/6

     | x+ 7 | = 3 - 5/6

     | x + 7| =  13/ 6

 roi chia thanh 2 truong hop la xong ok

Answer 2

còn các câu còn lại

Answer 3

\(c,1,7+|3,4-x|=6\)

\(\Leftrightarrow|3,4-x|=6-1,7\)

\(\Leftrightarrow|3,4-x|=5,7\)

\(\Leftrightarrow\orbr{\begin{cases}3,4-x=5,7\\3,4-x=-5,7\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=-2.3\\x=9,1\end{cases}}\)

Answer 4

\(d,5.|x-28|-3.5=\frac{1}{2}\)

\(\Leftrightarrow5.|x-28|=4\)

\(\Leftrightarrow|x-28|=\frac{4}{5}\)

\(\Leftrightarrow\orbr{\begin{cases}x-28=\frac{4}{5}\\x-28=-\frac{4}{5}\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=28.8\\x=27,2\end{cases}}\)

Answer 5

\(e,|x-\frac{1}{2}|.\left(x+1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}\orbr{\begin{cases}x-\frac{1}{2}=0\\\frac{1}{2}-x=0\end{cases}}\\x+1=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{2}\\x=-1\end{cases}}\)

Answer 6

a) \(3-\left|x+7\right|-\frac{1}{2}=\frac{1}{3}\)

\(\Rightarrow3-\left|x+7\right|=\frac{1}{2}+\frac{1}{3}\)

\(\Rightarrow3-\left|x+7\right|=\frac{5}{6}\)

\(\Rightarrow\left|x+7\right|=3-\frac{5}{6}\)

\(\Rightarrow\left|x+7\right|=\frac{13}{6}\)

\(\Rightarrow\orbr{\begin{cases}x+7=\frac{13}{6}\\x+7=\frac{-13}{6}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{13}{6}-7=\frac{13-42}{6}\\x=\frac{-13}{6}-7=\frac{-13-42}{6}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{-29}{6}\\x=\frac{-55}{6}\end{cases}}\)

b) \(\left|x-1,5\right|+\left|x-2,5\right|=0\)

Ta có: \(\left|x-1,5\right|\ge0;\left|x-2,5\right|\ge0\)

\(\Rightarrow\left|x-1,5\right|+\left|x-2,5\right|\ge0\)

Theo yêu cầu: \(\left|x-1,5\right|+\left|x-2,5\right|=0\)

\(\Rightarrow\hept{\begin{cases}\left|x-1,5\right|=0\\\left|x-2,5\right|=0\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}x-1,5=0\\x-2,5=0\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}x=1,5\\x=2,5\end{cases}}\)

Do giá trị x ko thể có cùng 2 giá trị nên vô lí.

c) \(1,7+\left|3,4-x\right|=6\)

\(\Rightarrow\left|3,4-x\right|=6-1,7\)

\(\Rightarrow\left|3,4-x\right|=4,3\)

\(\Rightarrow\orbr{\begin{cases}3,4-x=4,3\\3,4-x=-4,3\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=3,4-4,3=-0,9\\x=3,4-\left(-4,3\right)=7,7\end{cases}}\)

d) \(5.\left|x-28\right|-3,5=\frac{1}{2}\)

\(\Rightarrow5.\left|x-2,8\right|=\frac{1}{2}+\frac{7}{2}=4\)

\(\Rightarrow\left|x-2,8\right|=\frac{4}{5}\)

\(\Rightarrow\orbr{\begin{cases}x-2,8=0,8\\x-2,8=-0,8\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=3,6\\x=2\end{cases}}\)

e) \(\left|x-\frac{1}{2}\right|.\left(x+1\right)=0\)

\(\Rightarrow\orbr{\begin{cases}\left|x-\frac{1}{2}\right|=0\\x+1=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x-\frac{1}{2}=0\\x=-1\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{1}{2}\\x=-1\end{cases}}\)

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