Đáp án:
\(\begin{array}{l}
a,\,\,\,x < - \dfrac{4}{5}\\
b,\,\,\,x > \dfrac{{18}}{5}\\
c,\,\,\,x < 20\\
d,\,\,\,x \ge 15\\
e,\,\,\,x < - \dfrac{3}{4}\\
f,\,\,\,x < \dfrac{{12}}{5}
\end{array}\)
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
4\left( {2 - 3x} \right) - \left( {5 - x} \right) > 11 - x\\
\Leftrightarrow \left( {4.2 - 4.3x} \right) - 5 + x > 11 - x\\
\Leftrightarrow \left( {8 - 12x} \right) - 5 + x - \left( {11 - x} \right) > 0\\
\Leftrightarrow 8 - 12x - 5 + x - 11 + x > 0\\
\Leftrightarrow \left( {8 - 5 - 11} \right) + \left( { - 12x + x + x} \right) > 0\\
\Leftrightarrow - 8 - 10x > 0\\
\Leftrightarrow 8 + 10x < 0\\
\Leftrightarrow 10x < - 8\\
\Leftrightarrow x < - \dfrac{4}{5}\\
b,\\
2\left( {3 - x} \right) - 1,5.\left( {x - 4} \right) < 3 - x\\
\Leftrightarrow \left( {2.3 - 2.x} \right) - \left( {1,5.x - 1,5.4} \right) < 3 - x\\
\Leftrightarrow \left( {6 - 2x} \right) - \left( {1,5x - 6} \right) < 3 - x\\
\Leftrightarrow 6 - 2x - 1,5x + 6 - \left( {3 - x} \right) < 0\\
\Leftrightarrow 6 - 2x - 1,5x + 6 - 3 + x < 0\\
\Leftrightarrow \left( {6 + 6 - 3} \right) + \left( { - 2x - 1,5x + x} \right) < 0\\
\Leftrightarrow 9 - 2,5x < 0\\
\Leftrightarrow 2,5x > 9\\
\Leftrightarrow x > \dfrac{{18}}{5}\\
c,\\
\dfrac{{2x - 1}}{3} < \dfrac{{x + 6}}{2}\\
\Leftrightarrow 2.\left( {2x - 1} \right) < 3.\left( {x + 6} \right)\\
\Leftrightarrow 2.2x - 2.1 < 3.x + 3.6\\
\Leftrightarrow 4x - 2 < 3x + 18\\
\Leftrightarrow 4x - 2 - \left( {3x + 18} \right) < 0\\
\Leftrightarrow 4x - 2 - 3x - 18 < 0\\
\Leftrightarrow \left( {4x - 3x} \right) + \left( { - 2 - 18} \right) < 0\\
\Leftrightarrow x - 20 < 0\\
\Leftrightarrow x < 20\\
d,\\
\dfrac{{5.\left( {x - 1} \right)}}{6} - 1 \ge \dfrac{{2\left( {x + 1} \right)}}{3}\\
\Leftrightarrow \dfrac{{5.\left( {x - 1} \right) - 6}}{6} \ge \dfrac{{2.\left( {x + 1} \right)}}{3}\\
\Leftrightarrow \dfrac{{5x - 5 - 6}}{6} \ge \dfrac{{2.\left( {x + 1} \right)}}{3}\\
\Leftrightarrow \dfrac{{5x - 11}}{6} \ge \dfrac{{2x + 2}}{3}\\
\Leftrightarrow \dfrac{{5x - 11}}{6} - \dfrac{{2x + 2}}{3} \ge 0\\
\Leftrightarrow \dfrac{{\left( {5x - 11} \right) - 2.\left( {2x + 2} \right)}}{6} \ge 0\\
\Leftrightarrow \dfrac{{5x - 11 - \left( {4x + 4} \right)}}{6} \ge 0\\
\Leftrightarrow \dfrac{{5x - 11 - 4x - 4}}{6} \ge 0\\
\Leftrightarrow \dfrac{{x - 15}}{6} \ge 0\\
\Leftrightarrow x - 15 \ge 0\\
\Leftrightarrow x \ge 15\\
e,\\
\left( {2x + 3} \right)\left( {2x - 1} \right) > 4x\left( {x + 2} \right)\\
\Leftrightarrow 4{x^2} - 2x + 6x - 3 > 4{x^2} + 8x\\
\Leftrightarrow 4{x^2} + 4x - 3 > 4{x^2} + 8x\\
\Leftrightarrow 4{x^2} + 4x - 3 - \left( {4{x^2} + 8x} \right) > 0\\
\Leftrightarrow 4{x^2} + 4x - 3 - 4{x^2} - 8x > 0\\
\Leftrightarrow - 4x - 3 > 0\\
\Leftrightarrow 4x + 3 < 0\\
\Leftrightarrow 4x < - 3\\
\Leftrightarrow x < - \dfrac{3}{4}\\
f,\\
5.\left( {x - 1} \right) - x.\left( {7 - x} \right) < {x^2}\\
\Leftrightarrow \left( {5x - 5} \right) - \left( {7x - {x^2}} \right) < {x^2}\\
\Leftrightarrow 5x - 5 - 7 + {x^2} < {x^2}\\
\Leftrightarrow {x^2} + 5x - 12 < {x^2}\\
\Leftrightarrow 5x - 12 < 0\\
\Leftrightarrow 5x < 12\\
\Leftrightarrow x < \dfrac{{12}}{5}
\end{array}\)
