Tìm x biết 2|2x-3| =1/2 7,5-3|5-2x|= -4,5

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1. Đáp án:

   `2 | 2x – 3| = \frac{1}{2}`

   ` | 2x – 3| = \frac{1}{2}:2` 

   ` | 2x – 3| = \frac{1}{4}` 

   `⇒`\(\left[ \begin{array}{l}  2x – 3 = \frac{1}{4} \\  2x – 3 = -\frac{1}{4}\end{array} \right.\)

   `⇒`\(\left[ \begin{array}{l}  2x = \frac{1}{4}+ 3 \\  2x = -\frac{1}{4}+3\end{array} \right.\)

   `⇒`\(\left[ \begin{array}{l}  2x = \frac{13}{4} \\  2x  = \frac{11}{4}\end{array} \right.\)

   `⇒`\(\left[ \begin{array}{l}  x = \frac{13}{4} : 2\\  x  = \frac{11}{4} :2\end{array} \right.\)

   `⇒`\(\left[ \begin{array}{l}  x = \frac{13}{8} \\  x = \frac{11}{8}\end{array} \right.\)

   Vậy `x ∈ {\frac{13}{8} ; \frac{1}{8}}`

   `7,5 – 3|5 – 2x| = -4,5`

   `3|5 – 2x| = 7,5 + 4,5`

   ` 3|5 – 2x| = 12`

   `|5 – 2x| = 12 : 3`

   `|5 – 2x| = 4`

   `⇒`\(\left[ \begin{array}{l}  5 – 2x = 4 \\  5 – 2x = -4\end{array} \right.\)

   `⇒`\(\left[ \begin{array}{l} 2x = 5 -4 \\  2x =  5 + 4\end{array} \right.\)

   `⇒`\(\left[ \begin{array}{l} 2x = 1\\  2x =  9\end{array} \right.\)

   `⇒`\(\left[ \begin{array}{l} x = 1 : 2\\  x = 9 : 2\end{array} \right.\)

   `⇒`\(\left[ \begin{array}{l} x = 0,5 \\ x = 4,5\end{array} \right.\)

   Vậy `x ∈ {0,5 ; 4,5}`

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2. Giải thích các bước giải:

   `2|2x-3| =1/2`
   `=>|2x-3|=1/2:2`
   `=>|2x-3|=1/2. 1/2`
   `=>|2x-3|=1/4`
   TH`1`
   `2x-3=1/4`
   `=>2x=1/4+3`
   `=>2x=1/4+12/4`
   `=>2x=13/4`
   `=>x=13/4:2`
   `=>x=13/4. 1/2`
   `=>x=13/8`
   TH`2`
   `2x-3=-1/4`
   `=>2x=-1/4+3`
   `=>2x=-1/4+12/4`
   `=>2x=11/4`
   `=>x=11/4:2`
   `=>x=11/4. 1/2`
   `=>x=11/8`
   Vậy `x\in{13/8;11/8}`
   `7,5-3|5-2x|= -4,5`
   `=>3|5-2x|=7,5+4,5`
   `=>3|5-2x|=12`
   `=>|5-2x|=12:3`
   `=>|5-2x|=4`
   TH`1`
   `5-2x=4`
   `=>2x=5-4`
   `=>2x=1`
   `=>x=1/2`
   TH`2`
   `5-2x=-4`
   `=>2x=5+4`
   `=>2x=9`
   `=>x=9/2`
   Vậy `x\in{1/2;9/2}`

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