Сколько корней имеет уравнение: |x+2+|−x−4||−8=x
7/Задание № 3:
Сколько корней имеет уравнение: |x+2+|−x−4||−8=x?
РЕШЕНИЕ:
|x+2+|−x−4||−8=x
|x+2+|x+4||−8=x
Условию раскрытия моделей соответствуют только первый и третий корни 2 и -6.
ОТВЕТ: 2 корня
![\left \{
{{|x+2+x+4|-8=x,x \geq -4} \atop {|x+2-x-4|-8=x,x\ \textless \ -4}} \right. \\
\left \{ {{|2x+6|-8=x,x \geq -4} \atop {|-2|-8=x,x\ \textless \ -4}} \right. \\
\left \{ {{ \left \{ {{2x+6-8=x,x \geq -3} \atop {-2x-6-8=x,-4 \leq x \
\textless \ -3}} \right. } \atop {2-8=x,x\ \textless \ -4}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B%0A%7B%7B%7Cx%2B2%2Bx%2B4%7C-8%3Dx%2Cx+%5Cgeq+-4%7D+%5Catop+%7B%7Cx%2B2-x-4%7C-8%3Dx%2Cx%5C+%5Ctextless+%5C+-4%7D%7D+%5Cright.+%5C%5C%0A%5Cleft+%5C%7B+%7B%7B%7C2x%2B6%7C-8%3Dx%2Cx+%5Cgeq+-4%7D+%5Catop+%7B%7C-2%7C-8%3Dx%2Cx%5C+%5Ctextless+%5C+-4%7D%7D+%5Cright.+%5C%5C%0A%5Cleft+%5C%7B+%7B%7B+%5Cleft+%5C%7B+%7B%7B2x%2B6-8%3Dx%2Cx+%5Cgeq+-3%7D+%5Catop+%7B-2x-6-8%3Dx%2C-4+%5Cleq+x+%5C%0A%5Ctextless+%5C+-3%7D%7D+%5Cright.+%7D+%5Catop+%7B2-8%3Dx%2Cx%5C+%5Ctextless+%5C+-4%7D%7D+%5Cright.+ "\left \{
{{|x+2+x+4|-8=x,x \geq -4} \atop {|x+2-x-4|-8=x,x\ \textless \ -4}} \right. \\
\left \{ {{|2x+6|-8=x,x \geq -4} \atop {|-2|-8=x,x\ \textless \ -4}} \right. \\
\left \{ {{ \left \{ {{2x+6-8=x,x \geq -3} \atop {-2x-6-8=x,-4 \leq x \
\textless \ -3}} \right. } \atop {2-8=x,x\ \textless \ -4}} \right.")
![\left \{ {{ \left \{
{{2x-2=x,x \geq -3} \atop {-2x-14=x,-4 \leq x \ \textless \ -3}} \right. }
\atop {2-8=x,x\ \textless \ -4}} \right. \\ \left \{ {{ \left \{ {{x=2,x \geq
-3} \atop {3x=-14,-4 \leq x \ \textless \ -3}} \right. } \atop {x=-6,x\
\textless \ -4}} \right.](https://tex.z-dn.net/?f=%5Cleft+%5C%7B+%7B%7B+%5Cleft+%5C%7B%0A%7B%7B2x-2%3Dx%2Cx+%5Cgeq+-3%7D+%5Catop+%7B-2x-14%3Dx%2C-4+%5Cleq+x+%5C+%5Ctextless+%5C+-3%7D%7D+%5Cright.+%7D%0A%5Catop+%7B2-8%3Dx%2Cx%5C+%5Ctextless+%5C+-4%7D%7D+%5Cright.+%5C%5C+%5Cleft+%5C%7B+%7B%7B+%5Cleft+%5C%7B+%7B%7Bx%3D2%2Cx+%5Cgeq%0A-3%7D+%5Catop+%7B3x%3D-14%2C-4+%5Cleq+x+%5C+%5Ctextless+%5C+-3%7D%7D+%5Cright.+%7D+%5Catop+%7Bx%3D-6%2Cx%5C%0A%5Ctextless+%5C+-4%7D%7D+%5Cright.+ "\left \{ {{ \left \{
{{2x-2=x,x \geq -3} \atop {-2x-14=x,-4 \leq x \ \textless \ -3}} \right. }
\atop {2-8=x,x\ \textless \ -4}} \right. \\ \left \{ {{ \left \{ {{x=2,x \geq
-3} \atop {3x=-14,-4 \leq x \ \textless \ -3}} \right. } \atop {x=-6,x\
\textless \ -4}} \right.")
