## Rút gọn : A=3x-2|2x-5|

Question

Rút gọn : A=3x-2|2x-5|

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

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

2. Đáp án:

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