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\(x-\frac{3}{7}=\frac{-4}{3}\)
\(x=\frac{-4}{3}+\frac{3}{7}\)
\(x=-\frac{19}{21}\)
Vậy chọn đáp án \(a.\frac{-19}{21}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a,
\(5^{x+4}-3.5^{x+3}=2.5^{11}\)
\(\Rightarrow5^{x+3}\left(5-3\right)=2.5^{11}\)
\(\Rightarrow5^{x+3}2=2.5^{11}\)
\(\Rightarrow5^{x+3}=5^{11}\)
\(\Rightarrow x+3=11\)
\(\Rightarrow x=8\)
b, (Check lai xem de sai o dau khong nhe)
\(3.5^{x+2}+4.5^{x+3}=19.5^{10}\)
Dat 5x ra ben ngoai
\(\Rightarrow5^x.5^23+5^x:5^{-3}.4\)
\(\Rightarrow5^x\left(5^2.3+5^{-3}.4\right)\)
\(\Rightarrow5^x\left(5^{-3}.5^5.3+5^{-3}.4\right)\)
\(\Rightarrow5^x[5^{-3}\left(5^53+4\right)\)
\(\Rightarrow5^x[5^{-3}\left(3125.3+4\right)\)
\(\Rightarrow5^x\left(5^{-3}\right).9379\)
=> Khong tim duoc gia tri cua x \(\Rightarrow x\in\varnothing\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,x-\dfrac{5}{7}=\dfrac{19}{21}\\ x=\dfrac{34}{21}\\ b,\dfrac{5}{3}-\left|x-\dfrac{1}{5}\right|=\dfrac{1}{3}\\ \left|x-\dfrac{1}{5}\right|=\dfrac{4}{3}\\ TH1:x-\dfrac{1}{5}=\dfrac{4}{3}\\ x=\dfrac{23}{15}\\ TH2:x-\dfrac{1}{5}=-\dfrac{4}{3}\\ x=-\dfrac{17}{15}\\ c,x-\dfrac{2}{5}=\dfrac{1}{4}\\ x=\dfrac{13}{20}\\ d,5\sqrt{x}-30=15\\ 5\sqrt{x}=45\\ \sqrt{x}=9\\ x=9^2=81\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1 :
a/ Ta có :
\(C=\dfrac{19}{3}-\left|x+5\right|\)
Mà \(\left|x+5\right|\ge0\)
\(\Leftrightarrow C\le\dfrac{19}{3}\)
Để \(C\) đạt GTLN thì \(\left|x+5\right|\) đạt GTNN
Dấu "=" xảy ra khi :
\(\left|x+5\right|=0\)
\(\Leftrightarrow x=-5\)
Vậy GTLN của C = 19/3 khi x = -5
b/ Ta có :
\(D=\dfrac{-21}{7}-\left|4-x\right|\)
Mà \(\left|4-x\right|\ge0\)
\(\Leftrightarrow D\le\dfrac{-21}{7}\)
Để D đạt GTLN thì \(\left|4-x\right|\) đạt GTNN
Dấu "=" xảy ra khi :
\(\left|4-x\right|=0\)
\(\Leftrightarrow x=4\)
Vậy D đạt GTLN = -21/7 khi x = 4
Bài 2 :
a/ \(\left|x-\dfrac{4}{5}\right|=\dfrac{3}{4}\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{4}{5}=\dfrac{3}{4}\\x-\dfrac{4}{5}=-\dfrac{3}{4}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{31}{20}\\x=\dfrac{1}{20}\end{matrix}\right.\)
Vậy ...........
b/ \(6-\left|\dfrac{1}{2}-x\right|=\dfrac{2}{5}\)
\(\Leftrightarrow\left|\dfrac{1}{2}-x\right|=\dfrac{28}{15}\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{2}-x=\dfrac{28}{15}\\\dfrac{1}{2}-x=-\dfrac{28}{15}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{41}{30}\\x=\dfrac{71}{30}\end{matrix}\right.\)
Vậy ...