Tìm x : a ) | 3x – 5 | = | x + 2 | b ) 3x – 2x = -7-5 c ) | -2x – 5 | = | 3-x |

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1. a)

   `|3x-5|=|x+2|`

   `TH1: 3x-5=x+2`

   `⇔2x=7`

   `⇔x=7/2`

   `TH2: 3x-5=-x-2`

   `⇔4x=3`

   `⇔x=3/4`

   `TH3: -3x+5=x+2`

   `⇔-4x=-3`

   `⇔x=3/4 `

   `TH4: -3x+5=-x-2`

   `⇔-2x=-7`

   `⇔x=7/2`

   Vậy `x∈{7/2;3/4}`

   b)

   `3x-2x=-7-5`

   `⇔x=-12`

   Vậy `x=-12`

   c)

   `|-2x-5|=|3-x|`

   `TH1: -2x-5=3-x`

   `⇔-x=8`

   `⇔x=-8`

   `TH2: -2x-5=x-3`

   `⇔-3x=2`

   `⇔x=-2/3`

   `TH3: 2x+5=3-x`

   `⇔3x=-2`

   `⇔x=-2/3`

   `TH4: 2x+5=x-3`

   `⇔x=-8`

    Vậy `x∈{-8;-2/3}`

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2. $\text{a.|3x-5|=|x+2|}$

   ⇔\(\left[ \begin{array}{l}3x-5=x+2 \\3x-5=-x-2\end{array} \right.\) 

   ⇔\(\left[ \begin{array}{l}x=\dfrac{7}{2} \\x=\dfrac{3}{4}\end{array} \right.\) 

   $\text{Vậy}$ $x∈ \begin{Bmatrix} \dfrac{7}{2};\dfrac{3}{4} \end{Bmatrix}$

   $b.3x-2x=-7-5$

   $⇔x=-12$

   $\text{Vậy x=-12}$

   $c.|-2x-5|=|3-x|$

   ⇔\(\left[ \begin{array}{l}-2x-5=3-x\\-2x-5=x-3\end{array} \right.\) 

   ⇔\(\left[ \begin{array}{l}x=8\\x=\dfrac{-2}{3}\end{array} \right.\) 

   $\text{ Vậy}$ $x∈ \begin{Bmatrix} 8 ;\dfrac{-2}{3} \end{Bmatrix}$

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