|1/2x| = 3 - 2x
ĐKXĐ : 3 - 2x \(\ge\)0 => 2x \(\ge\) 3 => x \(\ge\)3/2
Ta có: |1/2x| = 3 - 2x
=> \(\orbr{\begin{cases}\frac{1}{2}x=3-2x\\\frac{1}{2}x=-3+2x\end{cases}}\)
=> \(\orbr{\begin{cases}\frac{1}{2}x+2x=3\\\frac{1}{2}x-2x=-3\end{cases}}\)
=> \(\orbr{\begin{cases}\frac{5}{2}x=3\\-\frac{3}{2}x=-3\end{cases}}\)
=> \(\orbr{\begin{cases}x=\frac{6}{5}\left(ktm\right)\\x=2\left(tm\right)\end{cases}}\)
=> x = 2
|5x| = x - 12
ĐKXĐ : x - 12 \(\ge\)0 => x \(\ge\)12
Ta có: |5x| = x - 12
=> \(\orbr{\begin{cases}5x=x-12\\5x=-x+12\end{cases}}\)
=> \(\orbr{\begin{cases}5x-x=-12\\5x+x=12\end{cases}}\)
=> \(\orbr{\begin{cases}4x=-12\\6x=12\end{cases}}\)
=> \(\orbr{\begin{cases}x=-3\\x=2\end{cases}}\)(ktm)
=> pt vô nghiệm
|2x - 5| = x + 1
ĐKXĐ: x + 1 \(\ge\)0 => x \(\ge\)-1
Ta có: |2x - 5| = x + 1
=> \(\orbr{\begin{cases}2x-5=x+1\\2x-5=-x-1\end{cases}}\)
=> \(\orbr{\begin{cases}2x-x=1+5\\2x+x=-1+5\end{cases}}\)
=> \(\orbr{\begin{cases}x=6\\3x=4\end{cases}}\)
=> \(\orbr{\begin{cases}x=6\\x=\frac{4}{3}\end{cases}}\)(tm)
Vậy ...
|7 - 2x| + 7 = 2x
=> |7 - 2x| = 2x - 7
ĐKXĐ: 2x - 7 \(\ge\)0 => 2x \(\ge\) 7 => x \(\ge\) 7/2
Ta có: |7 - 2x| = 2x - 7
=> \(\orbr{\begin{cases}7-2x=2x-7\\7-2x=7-2x\end{cases}}\)
=> 7 + 7 = 2x + 2x
hoặc x tùy ý (TMĐK)
=> 4x = 14 => x = 7/2
hoặc x tùy ý (Tm ĐK)
Vậy ...