Tìm x ∈ Q, biết rằng:
\(a){{11} \over {12}} - \left( {{2 \over 5} + x} \right) = {2 \over 3}\)
\(b)2{\rm{x}}.\left( {x - {1 \over 7}} \right) = 0\)
\(c){3 \over 4} + {1 \over 4}:x = {2 \over 5}\)
\(a){{11} \over {12}} - \left( {{2 \over 5} + x} \right) = {2 \over 3} \Leftrightarrow \left( {{2 \over 5} + x} \right) = {{11} \over {12}} - {2 \over 3}\)
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\( \Leftrightarrow {2 \over 5} + x = {{11} \over {12}} - {8 \over {12}} \Leftrightarrow {2 \over 5} + x = {1 \over 4}\)
\(\Rightarrow x = {1 \over 4} - {2 \over 5} \Leftrightarrow x = {5 \over {20}} - {8 \over {20}} \Leftrightarrow x = - {3 \over {20}}\)
\(b)2{\rm{x}}.\left( {x - {1 \over 7}} \right) = 0 \Leftrightarrow 2{\rm{x}} = 0\) hoặc \({\rm{x}} - {1 \over 7} = 0\)
\(\Rightarrow x = 0\) hoặc \(x = {1 \over 7}\). Vậy x = 0 hoặc \(x = {1 \over 7}\)
\(c){3 \over 4} + {1 \over 4}:x = {2 \over 5} \Leftrightarrow {1 \over 4}:x = {2 \over 5} - {3 \over 4} \Leftrightarrow {1 \over 4}:x = {8 \over {20}} - {{15} \over {20}}\)
\({1 \over 4}:x = {{ - 7} \over {20}} \Leftrightarrow x = {1 \over 4}:{{ - 7} \over {20}} \Leftrightarrow x = {1 \over 4}.{{ - 20} \over 7} = {{ - 5} \over 7}\)