Đáp án:
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Bài `4.1`
`a,`
`x = (-4)/7`
`↔ |x| = |-4/7|=4/7`
Vậy `|x|=4/7`
`b,`
`x = (-3)/(-11)`
`↔ |x| = | (-3)/(-11) | = 3/11`
Vậy `|x| = 3/11`
`c,`
`x = -0,749`
`↔ |x| = |-0,749| = 0,749`
Vậy `|x| = 0,749`
`d,`
`x = -5 1/7`
`-> x = (-36)/7`
`↔ |x| = |-36/7| = 36/7`
Vậy `|x| = 36/7`
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Câu `4.2`
`a,`
`|x| = 0`
`↔ x=0`
Vậy `x=0`
`b,`
`|x| = 1,375`
`↔` \(\left[ \begin{array}{l}x=1,375\\x=-1,375\end{array} \right.\)
Vậy `x=1,375` hoặc `x=-1,375`
`c,`
`|x| =1/5`
`↔` \(\left[ \begin{array}{l}x=\dfrac{1}{5}\\x=\dfrac{-1}{5}\end{array} \right.\)
Vậy `x=1/5` hoặc `x=(-1)/5`
`d,`
`|x| = 3 1/4`
`↔ |x| = 13/4`
`↔` \(\left[ \begin{array}{l}x=\dfrac{13}{4}\\x=\dfrac{-13}{4}\end{array} \right.\)
Vậy `x=13/4` hoặc `x=(-13)/4`
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Bài `4.3`
`a,`
`|x - 1,5| = 2`
`↔` \(\left[ \begin{array}{l}x-1,5=2\\x-1,5=-2\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}x=2 + 1,5\\x=-2+1,5\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}x=3,5\\x=-0,5\end{array} \right.\)
Vậy `x=3,5` hoặc `x=-0,5`
`b,`
`|x + 3/4| - 1/2 =0`
`↔ |x+3/4| = 0+1/2`
`↔ |x+3/4|=1/2`
`↔` \(\left[ \begin{array}{l}x+\dfrac{3}{4}=\dfrac{1}{2}\\x+\dfrac{3}{4}=\dfrac{-1}{2}\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}x=\dfrac{1}{2}-\dfrac{3}{4}\\x=\dfrac{-1}{2}-\dfrac{3}{4}\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}x=\dfrac{-1}{4}\\x=\dfrac{-5}{4}\end{array} \right.\)
Vậy `x=(-1)/4` hoặc `x=(-5)/4`
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Bài `4.4`
`A = 5 + |1/3-x|`
Vì `|1/3 - x| ≥0∀x`
`↔ 5 + |1/3 - x| ≥ 0 ∀x`
`↔ A ≥ 5∀ x`
`↔ min A = 5`
Dấu "`=`" xảy ra khi :
`↔1/3-x=0`
`↔x=1/3-0`
`↔x=1/3`
Vậy `min A =5 ↔ x=1/3`
