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Tìm x trong các tỉ lệ thức sau:
a) \({\rm{}}3,8:(2{\rm{x}}) = {1 \over 4}:2{2 \over 3}\)
b) \(\left( {0,25{\rm{x}}} \right):3 = {5 \over 6}:0,125\)
c) 0,01: 2,5 = (0,75x): 0,75
d) \({\rm{}}1{1 \over 3}:0,8 = {2 \over 3}:(0,1{\rm{x}})\)
\(\eqalign{
& a)3,8:(2{\rm{x}}) = {1 \over 4}:2{2 \over 3} \cr
& \Leftrightarrow \left( {2{\rm{x}}} \right).{1 \over 4} = 3,8.2{2 \over 3} \cr
& \Leftrightarrow \left( {2{\rm{x}}} \right).{1 \over 4} = {{19} \over 5}.{8 \over 3} \cr
& \Leftrightarrow x = {{152} \over {15}}:{1 \over 2} = {{152} \over {15}}.{2 \over 1} \cr
& \Leftrightarrow x = 20{4 \over {15}} \cr} \)
b) \(\left( {0,25{\rm{x}}} \right):3 = {5 \over 6}:0,125\)
\( \Leftrightarrow \left( {0,25{\rm{x}}} \right).0,125 = 3.{5 \over 6}\)
\( \Leftrightarrow \left( {0,25{\rm{x}}} \right).0,125 = 2,5\)
\( \Leftrightarrow 0,25{\rm{x}} = 2,5:0,125\)
\( \Leftrightarrow 0,25{\rm{x}} = 20\)
\( \Leftrightarrow x = 20:0,25 = 80\)
c) \(0,01:2,5 = \left( {0,75x} \right):0,75\)
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\( \Leftrightarrow \left( {0,75{\rm{x}}} \right).2,5 = 0,01.0,75\)
\( \Leftrightarrow \left( {0,75{\rm{x}}} \right) = (0,01.0,75):2,5\)
\( \Leftrightarrow 0,75{\rm{x}} = 0,003\)
\( \Leftrightarrow x = 0,003:0,75\)
\( \Leftrightarrow x = 0,004\)
d) \({\rm{}}1{1 \over 3}:0,8 = {2 \over 3}:(0,1{\rm{x}})\)
\( \Leftrightarrow {4 \over 3}.\left( {0,1{\rm{x}}} \right) = {4 \over 5}.{2 \over 3}\)
\( \Leftrightarrow \left( {0,1{\rm{x}}} \right) = {4 \over 5}.{2 \over 3}:{4 \over 3}\)
\( \Leftrightarrow 0.1{\rm{x}} = {8 \over {15}}.{3 \over 4}\)
\( \Leftrightarrow {1 \over {10}}x = {2 \over 5}\)
\(\Leftrightarrow x = {2 \over 5}:{1 \over {10}} = {2 \over 5}.{{10} \over 1} = 4\)