Question

[Trần Thảo Anh]

1. tìm x biết

a, | 2x-5 | = 4

b, \(\frac{1}{3}\)\(-\)\(|\)\(\frac{5}{4}\)\(-\)2x\(|\)= \(\frac{1}{4}\)

c,\(|\)\(-\)\(\frac{2}{3}\)\(|\)\(+\)\(|\)x\(-\)\(\frac{1}{3}\)\(|\)\(=\)\(|\)\(-\)1\(|\)\(-\)\(|\)\(-\)\(\frac{1}{3}\)\(|\)

d, \(|\)\(-\)\(\frac{1}{2}\)\(|\)\(-\)\(|\)x \(+\)\(\frac{1}{4}\)\(|\)\(=\)\(|\)\(-\)\(|\)\(\frac{-3}{4}\)\(|\)

2. tìm x biết 

a, \(|\)x\(-\)1\(|\)\(=\)3x \(+\)2

b, \(|\)9\(+\)x\(|\)\(=\)2x

c, \(|\)x \(+\)6\(|\)\(-\)9\(=\)2x

3. tìm x biết

a, \(|\)\(\frac{7}{5}\)x \(+\)\(\frac{2}{3}\)\(|\)\(=\)\(|\)\(\frac{4}{3}\)x \(-\)\(\frac{1}{4}\)\(|\)

b, \(|\)\(\frac{7}{8}\)x \(+\)\(\frac{5}{6}\)\(|\)\(-\)\(|\)\(\frac{1}{2}\)x \(+\)5\(|\)\(=\)0

4. tìm x và y biết

a, \(|\)x\(-\)19\(|\)\(+\)\(|\)y\(-\)20\(|\)\(=\)0

b, \(|\)x²\(-\)4\(|\)\(+\)\(|\)y²\(-\)9\(|\)\(=\)0

c, \(|\)x\(-\)y\(|\)\(+\)\(|\)x² \(-\)25\(|\)\(=\)0

Answer 1

[Trí Tiên]

dài :vv

a) \(\left|2x-5\right|=4\Leftrightarrow\hept{\begin{cases}2x-5=4\\2x-5=-4\end{cases}\Leftrightarrow\hept{\begin{cases}2x=9\\2x=1\end{cases}\Leftrightarrow}\hept{\begin{cases}x=\frac{9}{2}\\x=\frac{1}{2}\end{cases}}}\)

b) \(\frac{1}{3}-\left|\frac{5}{4}-2x\right|=\frac{1}{4}\)

\(\Leftrightarrow\left|\frac{5}{4}-2x\right|=\frac{1}{12}\Leftrightarrow\hept{\begin{cases}\frac{5}{4}-2x=\frac{1}{12}\\\frac{5}{4}-2x=-\frac{1}{12}\end{cases}\Leftrightarrow\hept{\begin{cases}2x=\frac{7}{6}\\2x=\frac{4}{3}\end{cases}}\Leftrightarrow\hept{\begin{cases}x=\frac{7}{12}\\x=\frac{2}{3}\end{cases}}}\)

Answer 2

[ᵛᶰシHắ¢ღHσàиɢღTнιêиღуυм★彡]

Bài 1 :

a) \(|2x-5|=4\)

\(\Rightarrow\orbr{\begin{cases}2x-5=4\\2x-5=-4\end{cases}\Rightarrow}\orbr{\begin{cases}2x=9\\2x=1\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{9}{2}\\x=\frac{1}{2}\end{cases}}}\)

b) \(\frac{1}{3}-\left|\frac{5}{4}-2x\right|=\frac{1}{4}\)

\(\Rightarrow\left|\frac{5}{4}-2x\right|=\frac{1}{12}\)

\(\Rightarrow\orbr{\begin{cases}\frac{5}{4}-2x=\frac{1}{12}\\\frac{5}{4}-2x=-\frac{1}{12}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}2x=\frac{7}{6}\\2x=\frac{4}{3}\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{7}{12}\\x=\frac{2}{3}\end{cases}}}\)

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

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

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

\(\Rightarrow\left|x-\frac{1}{3}\right|=0\Rightarrow x-\frac{1}{3}=0\Rightarrow x=\frac{1}{3}\)

d) \(\left|-\frac{1}{2}\right|-\left|x+\frac{1}{4}\right|=\left|-\frac{3}{4}\right|\)

\(\Rightarrow\frac{1}{2}-\left|x+\frac{1}{4}\right|=\frac{3}{4}\)

\(\Rightarrow\left|x+\frac{1}{4}\right|=-\frac{1}{4}\)

Vì \(\left|x\right|\ge0\Rightarrow\)ko có gtri nào của x thỏa mãn đề bài

Bài 2 :

a) \(\left|x-1\right|=3x+2\)

\(\Rightarrow\orbr{\begin{cases}x-1=3x+2\\x-1=-3x-2\end{cases}\Rightarrow\orbr{\begin{cases}x-3x=2+1\\x+3x=-2+1\end{cases}}}\)

\(\Rightarrow\orbr{\begin{cases}-2x=3\\4x=-1\end{cases}\Rightarrow}\orbr{\begin{cases}x=\frac{-3}{2}\\x=\frac{-1}{4}\end{cases}}\)

b|) \(\left|9+x\right|=2x\Rightarrow\orbr{\begin{cases}9+x=2x\\9+x=-2x\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x-2x=-9\\x+2x=-9\end{cases}\Rightarrow\orbr{\begin{cases}-x=-9\\3x=-9\end{cases}\Rightarrow}\orbr{\begin{cases}x=9\\x=-3\end{cases}}}\)

c) \(\left|x+6\right|-9=2x\Rightarrow\left|x+6\right|=2x+9\)

\(\Rightarrow\orbr{\begin{cases}x+6=2x+9\\x+6=-2x-9\end{cases}\Rightarrow}\orbr{\begin{cases}x-2x=9-6\\x+2x=-9-6\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}-x=3\\3x=-15\end{cases}\Rightarrow\orbr{\begin{cases}x=-3\\x=-5\end{cases}}}\)

Cậu có thể tham khảo bài làm trên đây ạ, chúc cậu học tốt ^^