Bài 16 trang 9 SBT toán 7 tập 1

Đề bài

Tìm \(x ∈ Q\), biết rằng:

\(\displaystyle a)\;{{11} \over {12}} - \left( {{2 \over 5} + x} \right) = {2 \over 3}\)

\(\displaystyle b)\;2{\rm{x}}.\left( {x - {1 \over 7}} \right) = 0\)

\(\displaystyle c)\;{3 \over 4} + {1 \over 4}:x = {2 \over 5}\)

Lời giải

\(\displaystyle a)\;{{11} \over {12}} - \left( {{2 \over 5} + x} \right) = {2 \over 3} \)

 \(\displaystyle  \left( {{2 \over 5} + x} \right) = {{11} \over {12}} - {2 \over 3}\) 

 \( \displaystyle {2 \over 5} + x = {{11} \over {12}} - {8 \over {12}}\)

 \(\displaystyle {2 \over 5} + x = {1 \over 4}\)

 \(\displaystyle x = {1 \over 4} - {2 \over 5} \)

 \(\displaystyle x = {5 \over {20}} - {8 \over {20}} \)

 \(\displaystyle x =  - {3 \over {20}}\)

\(\displaystyle b)\;2{\rm{x}}.\left( {x - {1 \over 7}} \right) = 0\)

 \(\Rightarrow  2{\rm{x}} = 0\) hoặc \(\displaystyle {\rm{x}} - {1 \over 7} = 0\)

 \(\Rightarrow x = 0\) hoặc \(\displaystyle x = {1 \over 7}\).

Vậy \(x = 0\) hoặc \(\displaystyle x = {1 \over 7}\)

\(\displaystyle c)\;{3 \over 4} + {1 \over 4}:x = {2 \over 5}\)

 \(\displaystyle {1 \over 4}:x = {2 \over 5} - {3 \over 4}\)

 \(\displaystyle {1 \over 4}:x = {8 \over {20}} - {{15} \over {20}}\)

 \(\displaystyle {1 \over 4}:x = {{ - 7} \over {20}}\)

 \(\displaystyle x = {1 \over 4}:{{ - 7} \over {20}} \)

 \(\displaystyle x = {1 \over 4}.{{ - 20} \over 7} = {{ - 5} \over 7}\)


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