Đáp án:
`b)` `x=-5/2` hoặc `x=-11/2`
`c)` `(x-1)(x+3/2)>0` với mọi `x` ngoài `2` giá trị `x=1` hoặc `x=-3/2`
Giải thích các bước giải:
`b)` `1 1/2-|1/2*x+2|=0,75`
`⇒ 3/2-|1/2x+2| =3/4`
`⇒ |1/2x+2| =3/2-3/4`
`⇒ |1/2x+2| =(6-3)/4`
`⇒ |1/2x+2| =3/4`
`⇒`\(\left[ \begin{array}{l}\dfrac{1}{2}x+2=\dfrac{3}{4}\\\dfrac{1}{2}x+2=-\dfrac{3}{4}\end{array} \right.\) `⇒`\(\left[ \begin{array}{l}\dfrac{1}{2}x=\dfrac{3}{4}-2\\\dfrac{1}{2}x=-\dfrac{3}{4}-2\end{array} \right.\) `⇒`\(\left[ \begin{array}{l}\dfrac{1}{2}x=\dfrac{-5}{4}\\\dfrac{1}{2}x=-\dfrac{11}{4}\end{array} \right.\)
`⇒`\(\left[ \begin{array}{l}x=\dfrac{-5}{4}:\dfrac{1}{2}\\\dfrac{-11}{4}:\dfrac{1}{2}\end{array} \right.\)`⇒`\(\left[ \begin{array}{l}x=\dfrac{-5}{4}.2=\dfrac{-5}{2}\\x=\dfrac{-11}{4}.2=\dfrac{-11}{2}\end{array} \right.\)
Vậy `x=(-5)/2` hoặc `x=(-11)/2`
`c)` `(x-1)(x+3/2)>0`
Dấu `=` xảy ra khi \(\left[ \begin{array}{l}x-1=0\\x+\dfrac{3}{2}=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=1\\x=-\dfrac{3}{2}\end{array} \right.\)
Vậy `(x-1)(x+3\2)>0` với mọi `x` ngoài `2` giá trị `x=1` và `x=-3/2`
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