1. m(x-m) ≤ 4x +5 2. (x+1)k+x<(3x+4) 3.( a+1)x+a+3 ≥4x+1 4. m(x-m)>2(4-x) 5. 3x+m^2 >m(x+3)

0 bình luận về “1. m(x-m) ≤ 4x +5 2. (x+1)k+x<(3x+4) 3.( a+1)x+a+3 ≥4x+1 4. m(x-m)>2(4-x) 5. 3x+m^2 >m(x+3)”

1. Đáp án:

   $\begin{array}{l}
   1)m\left( {x – m} \right) \le 4x + 5\\
    \Rightarrow mx – {m^2} \le 4x + 5\\
    \Rightarrow \left( {m – 4} \right).x \le {m^2} + 5\\
    + Khi:m \ge 4 \Rightarrow x \le \dfrac{{{m^2} + 5}}{{m – 4}}\\
    + Khi:m < 4 \Rightarrow x \ge \dfrac{{{m^2} + 5}}{{m – 4}}\\
   2)\left( {x + 1} \right).k + x < 3x + 4\\
    \Rightarrow \left( {k + 1 – 3} \right).x < 4 – k\\
    \Rightarrow \left( {k – 2} \right).x < 4 – k\\
    + Khi:k \ge 2 \Rightarrow x < \dfrac{{4 – k}}{{k – 2}}\\
    + Khi:k < 2 \Rightarrow x > \dfrac{{4 – k}}{{k – 2}}\\
   3)\left( {a + 1} \right).x + a + 3 \ge 4x + 1\\
    \Rightarrow \left( {a + 1 – 4} \right).x \ge  – a – 3 + 1\\
    \Rightarrow \left( {a – 3} \right).x \ge  – a – 2\\
    + Khi:a \ge 3 \Rightarrow x \ge \dfrac{{ – a – 2}}{{a – 3}}\\
    + Khi:a < 3 \Rightarrow x \le \dfrac{{ – a – 2}}{{a – 3}}\\
   4)m\left( {x – m} \right) > 2\left( {4 – x} \right)\\
    \Rightarrow \left( {m + 2} \right).x > {m^2} + 8\\
    + Khi:m \ge  – 2 \Rightarrow x > \dfrac{{{m^2} + 8}}{{m + 2}}\\
    + Khi:m <  – 2 \Rightarrow x < \dfrac{{{m^2} + 8}}{{m + 2}}\\
   5)3x + {m^2} > m\left( {x + 3} \right)\\
    \Rightarrow \left( {m – 3} \right).x < {m^2} – 3m\\
    + Khi:m = 3\left( {ktm} \right)\\
    + Khi:m > 3 \Rightarrow x < m\\
    + Khi:m < 3 \Rightarrow x > m
   \end{array}$

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