a) |x-5|=13-2x b)|5x-1|=x-12 c)|-2x|=3x+4 d)|2x-1|=6-x

Question

a) |x-5|=13-2x
b)|5x-1|=x-12
c)|-2x|=3x+4
d)|2x-1|=6-x

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7 phút 2021-10-09T23:54:22+00:00 2 Answers 0 views 0

1. Đáp án:

Giải thích các bước giải:

2. Đáp án:

d. $$\left[ \begin{array}{l} x = \dfrac{7}{3}\\ x = – 5 \end{array} \right.$$

Giải thích các bước giải:

$$\begin{array}{l} a.\left| {x – 5} \right| = 13 – 2x\\ \to \left[ \begin{array}{l} x – 5 = 13 – 2x\left( {x \ge 5} \right)\\ x – 5 = – 13 + 2x\left( {x < 5} \right) \end{array} \right.\\ \to \left[ \begin{array}{l} 3x = 18\\ x = 8\left( l \right) \end{array} \right.\\ \to x = 6\left( {TM} \right)\\ b.\left| {5x – 1} \right| = x – 12\\ \to \left[ \begin{array}{l} 5x – 1 = x – 12\left( {x \ge \dfrac{1}{5}} \right)\\ 5x – 1 = – x + 12\left( {x < \dfrac{1}{5}} \right) \end{array} \right.\\ \to \left[ \begin{array}{l} 4x = – 11\\ 6x = 13 \end{array} \right.\\ \to \left[ \begin{array}{l} x = – \dfrac{{11}}{4}\left( l \right)\\ x = \dfrac{{13}}{6}\left( l \right) \end{array} \right. \end{array}$$

⇒ Phương trình vô nghiệm

$$\begin{array}{l} c.\left| { – 2x} \right| = 3x + 4\\ \to \left[ \begin{array}{l} – 2x = 3x + 4\left( {x \ge 0} \right)\\ 2x = 3x + 4\left( {x < 0} \right) \end{array} \right.\\ \to \left[ \begin{array}{l} 5x = – 4\\ x = – 4 \end{array} \right.\\ \to \left[ \begin{array}{l} x = – \dfrac{4}{5}\left( l \right)\\ x = – 4\left( {TM} \right) \end{array} \right.\\ d.\left| {2x – 1} \right| = 6 – x\\ \to \left[ \begin{array}{l} 2x – 1 = 6 – x\left( {x \ge \dfrac{1}{2}} \right)\\ 2x – 1 = – 6 + x\left( {x < \dfrac{1}{2}} \right) \end{array} \right.\\ \to \left[ \begin{array}{l} 3x = 7\\ x = – 5 \end{array} \right.\\ \to \left[ \begin{array}{l} x = \dfrac{7}{3}\\ x = – 5 \end{array} \right. \end{array}$$