Bài 1: Tính
a) \(\left[ {{5 \over 3} – \left( { – {1 \over 4}} \right):1{1 \over 5}} \right]:\left( {{5 \over 8} + {9 \over 4}} \right);\)
b) \(1 – \left\{ {1:\left[ {2 + 1:\left( {1 – {1 \over 2}} \right)} \right]} \right\}.\)
Bài 2: Tìm x biết: \({1 \over 3}x + {2 \over 5}\left( {x + 1} \right) = 0.\)
Bài 3: Tìm các giá trị của x biết: \({{x – 7} \over 2} < 0.\)
Bài 1: a) \(\left[ {{5 \over 3} – \left( { – {1 \over 4}} \right):1{1 \over 5}} \right]:\left( {{5 \over 8} + {9 \over 4}} \right) \)
\(= \left[ {{5 \over 3} – \left( { – {1 \over 4}} \right):{6 \over 5}} \right]:\left( {{{5 + 18} \over 8}} \right)\)
\( = \left[ {{5 \over 3} – \left( { – {1 \over 4}} \right).{5 \over 6}} \right]:{{23} \over 8} \)
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\(= \left( {{5 \over 3} + {5 \over {24}}} \right):{{23} \over 8} \)
\(= \left( {{{40 + 5} \over {24}}} \right):{{23} \over 8} \)
\(= {{45} \over {24}}.{8 \over {23}} = {{15} \over {23}}. \)
b) \(1 – \left\{ {1:\left[ {2 + 1:\left( {1 – {1 \over 2}} \right)} \right]} \right\} \)
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\(= 1 – \left[ {1:\left( {2 + 1:{1 \over 2}} \right)} \right]\)
\( = 1 – \left[ {1:\left( {2 + 2} \right)} \right] = 1 – \left( {1:4} \right) \)
\(= 1 – {1 \over 4} = {{4 – 1} \over 4} = {3 \over 4}.\)
Bài 2: \({1 \over 3}x + {2 \over 5}\left( {x + 1} \right) = 0\)
\(\Rightarrow {1 \over 3}x + {2 \over 5}x + {2 \over 5} = 0\)
\( \Rightarrow {1 \over 2}x + {2 \over 5}x = – {2 \over 5}\)
\(\Rightarrow {{5x + 6x} \over {15}} = – {2 \over 5}\)
\(\Rightarrow {{11} \over {15}}x = – {2 \over 5} \)
\( \Rightarrow x = – {2 \over 5}:{{11} \over {15}}\)
\(\Rightarrow x = – {2 \over 5}.{{15} \over {11}}\)
\(\Rightarrow x = – {6 \over {11}}. \)
Bài 3: Vì \(2 > 0\) nên \({{x – 7} \over 2} < 0\) khi \(x – 7 < 0 \Rightarrow x < 7.\)
