Rút gọn : A=3x-2|2x-5|

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Rút gọn : A=3x-2|2x-5|

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Tryphena 1 year 2020-10-13T16:33:45+00:00 2 Answers 86 views 0

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    0
    2020-10-13T16:35:20+00:00

    `A = 3x – 2 | 2x – 5 |`

    TH1: `2x – 5 ≥ 0` `⇔ x ≥ 5/2` `⇒2x – 5 = 2x – 5`

    `⇒A = 3x – 2(2x – 5)`

    `⇒A = 3x – 4x + 10`

    `⇒A = -x + 10 = 10 – x`

    TH2: `2x – 5 < 0` `⇔ x < 5/2` `⇒2x – 5 = -2x + 5`

    `⇒A = 3x – 2(-2x + 5)`

    `⇒A = 3x + 4x – 10`

    `⇒A = 7x – 10`

    Vậy \(\left[ \begin{array}{l}A=10-x \text{ (Nếu x ≥ }\frac{5}{2})\\A=7x-10\text{ (Nếu x < }\frac{5}{2})\end{array} \right.\) 

    0
    2020-10-13T16:35:22+00:00

    Đáp án:

    $\begin{array}{l}
    A = 3x – 2\left| {2x – 5} \right|\\
     + Khi:2x – 5 \ge 0 \Rightarrow x \ge \dfrac{5}{2}\\
     \Rightarrow \left| {2x – 5} \right| = 2x – 5\\
     \Rightarrow A = 3x – 2\left( {2x – 5} \right)\\
     = 3x – 4x + 10\\
     = 10 – x\\
     + Khi:2x – 5 < 0 \Rightarrow x < \dfrac{5}{2}\\
     \Rightarrow \left| {2x – 5} \right| =  – 2x + 5\\
     \Rightarrow A = 3x – 2\left( { – 2x + 5} \right)\\
     = 3x + 4x – 10\\
     = 7x – 10\\
    Vay\,A = 10 – x\,\left( {khi:x \ge \dfrac{5}{2}} \right)\\
    A = 7x – 10\left( {khi:x < \dfrac{5}{2}} \right)
    \end{array}$

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )