Advertisements (Quảng cáo)
Giải các phương trình sau:
a. \({{x – 3} \over 5} = 6 – {{1 – 2x} \over 3}\)
b. \({{3x – 2} \over 6} – 5 = {{3 – 2\left( {x + 7} \right)} \over 4}\)
c. \(2\left( {x + {3 \over 5}} \right) = 5 – \left( {{{13} \over 5} + x} \right)\)
d. \({{7x} \over 8} – 5\left( {x – 9} \right) = {{20x + 1,5} \over 6}\)
a. \({{x – 3} \over 5} = 6 – {{1 – 2x} \over 3}\)
\( \Leftrightarrow 3\left( {x – 3} \right) = 6.15 – 5\left( {1 – 2x} \right)\)
\(\eqalign{ & \Leftrightarrow 3x – 9 = 90 – 5 + 10x \cr & \Leftrightarrow 3x – 10x = 90 – 5 + 9 \cr & \Leftrightarrow – 7x = 94 \Leftrightarrow x = – {{94} \over 7} \cr} \)
Phương trình có nghiệm
b. \(\eqalign{ & {{3x – 2} \over 6} – 5 = {{3 – 2\left( {x + 7} \right)} \over 4} \Leftrightarrow 2\left( {3x – 2} \right) – 5.12 = 3\left[ {3 – 2\left( {x + 7} \right)} \right] \cr & \Leftrightarrow 6x – 4 – 60 = 9 – 6\left( {x + 7} \right) \Leftrightarrow 6x – 64 = 9 – 6x – 42 \cr & \Leftrightarrow 6x + 6x = 9 – 42 + 64 \Leftrightarrow 12x = 31 \Leftrightarrow x = {{31} \over {12}} \cr} \)
Phương trình có nghiệm $x = {{31} \over {12}}\)
c. \(\eqalign{ & 2\left( {x + {3 \over 5}} \right) = 5 – \left( {{{13} \over 5} + x} \right) \cr & \Leftrightarrow 2x + {6 \over 5} = {{25} \over 5} – {{13} \over 5} – x \cr} \)
\(\eqalign{ & \Leftrightarrow 2x + {6 \over 5} = {{12} \over 5} – x \cr & \Leftrightarrow 2x + x = {{12} \over 5} – {6 \over 5} \cr & \Leftrightarrow 3x = {6 \over 5} \cr & \Leftrightarrow x = {2 \over 5} \cr} \)
Phương trình có nghiệm
d. \({{7x} \over 8} – 5\left( {x – 9} \right) = {{20x + 1,5} \over 6}\)
\( \Leftrightarrow 3.7x – 24.5\left( {x – 9} \right) = 4\left( {20x + 1,5} \right)\)
\(\eqalign{ & \Leftrightarrow 21x – 120\left( {x – 9} \right) = 80x + 6 \cr & \Leftrightarrow 21x – 120x + 1080 = 80x + 6 \cr & \Leftrightarrow 21x – 120x – 80x = 6 – 1080 \cr & \Leftrightarrow – 179x = – 1074 \cr & \Leftrightarrow x = 6 \cr} \)
Phương trình có nghiệm x = 6