Đáp án:
a) `x>=0`
b) \(\left[ \begin{array}{l}x≥2\\x≤-\dfrac{1}{2}\end{array} \right.\)
Giải thích các bước giải:
a) `(x-2)/6-(x-1)/3 <=x/2`
`=>((x-2)-2(x-1))/6 <=(3x)/6`
`=>(x-2)-2(x-1) <=3x`
`=>x-2-2x+2 <=3x`
`=>-x <=3x`
`=>-x-3x<=0`
`=>-4x<=0`
`=>x>=0`
b) `(x-2)(2x+1)>=0`
`=>`\(\left[ \begin{array}{l}\left\{\begin{matrix} x-2≥0 \\ 2x+1≥0 \end{matrix}\right.\\\left\{\begin{matrix} x-2≤0 \\ 2x+1≤0 \end{matrix}\right.\end{array} \right.\) `=>`\(\left[ \begin{array}{l}\left\{\begin{matrix} x≥2 \\ 2x≥-1 \end{matrix}\right.\\\left\{\begin{matrix} x≤2 \\ 2x≤-1 \end{matrix}\right.\end{array} \right.\) `=>`\(\left[ \begin{array}{l}\left\{\begin{matrix} x≥2 \\ x≥\dfrac{-1}{2} \end{matrix}\right.\\\left\{\begin{matrix} x≤2 \\ x≤\dfrac{-1}{2} \end{matrix}\right.\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x≥2\\x≤\dfrac{-1}{2}\end{array} \right.\)
Vậy `x>=2` hoặc `x<=-1/2.`
