1)
`|x+3|=x+3`
`<=>`\(\left[ \begin{array}{l}x+3=x+3(ĐKXĐ:x≥-3)\\x+3=-(x+3)(ĐKXĐ:x≤-3)\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x-x=3-3\\x+3=-x-3\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}0=0 (luôn đúng)\\x+x=-3-3\end{array} \right.\)
`=>2x=-6`
`<=>x=-3` (TM)
Vậy: `S={-3}`
2)
`|2x-1|=1-2x`
`<=>`\(\left[ \begin{array}{l}2x-1=1-2x(ĐKXĐ:x≥\dfrac{1}{2} )\\2x-1=-(1-2x)(ĐKXĐ:x≤\dfrac{1}{2} )\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}2x+2x=1+1\\2x-1=-1+2x\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}4x=2\\2x-2x=-1+1\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=\dfrac{1}{2}(TM)\\0=0 (luôn đúng)\end{array} \right.\)
Vậy: `S={1/2}`
3)
`|2x-9|=2x-9`
`<=>`\(\left[ \begin{array}{l}2x-9=2x-9(ĐKXĐ:x≥\dfrac{9}{2})\\2x-9=-(2x-9)(ĐKXĐ:x≤\dfrac{9}{2} )\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}2x-2x=-9+9\\2x-9=-2x+9\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}0=0(luôn đúng)\\2x+2x=9+9\end{array} \right.\)
`=>4x=18`
`<=>x=9/2` (TM)
Vậy: `S={9/2}`
4)
`|7-5x|=5x-7`
`<=>`\(\left[ \begin{array}{l}7-5x=5x-7(ĐKXĐ:x≤\dfrac{7}{5})\\7-5x=-(5x-7)(ĐKXĐ:x≥\dfrac{7}{5} )\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}-5x-5x=-7-7\\7-5x=-5x+7\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}-10x=-14\\-5x+5x=7-7\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=\dfrac{7}{5}(TM)\\0=0(luôn đúng)\end{array} \right.\)
Vậy: `S={7/5}`
