Условие можно прочитать по-разному:
1)
![2x + \frac{5}{7} + 3x - \frac{1}{2} = x + 1 \\ \\ 5x + \frac{5*2 - 1*7}{14} = x + 1 \\ \\ 5x + \frac{3}{14} = x + 1 \\ \\ 5x - x = 1 - \frac{3}{14} \\ \\ 4x = \frac{11}{14} \\ \\ x = \frac{11}{14} : 4 = \frac{11}{14} * \frac{1}{4} \\ \\ x = \frac{11}{56}](https://tex.z-dn.net/?f=2x+%2B+%5Cfrac%7B5%7D%7B7%7D++%2B+3x++-++%5Cfrac%7B1%7D%7B2%7D+%3D+x++%2B+1+%5C%5C++%5C%5C+%0A5x++%2B++%5Cfrac%7B5%2A2+-+1%2A7%7D%7B14%7D++%3D+x++%2B+1+%5C%5C++%5C%5C+%0A5x++%2B++%5Cfrac%7B3%7D%7B14%7D+%3D+x++%2B+1+%5C%5C++%5C%5C+%0A5x++-+x++%3D++1++-++%5Cfrac%7B3%7D%7B14%7D++%5C%5C++%5C%5C+%0A4x++%3D++%5Cfrac%7B11%7D%7B14%7D++%5C%5C++%5C%5C+%0Ax+%3D++%5Cfrac%7B11%7D%7B14%7D+%3A++4+%3D++%5Cfrac%7B11%7D%7B14%7D++%2A++%5Cfrac%7B1%7D%7B4%7D++%5C%5C++%5C%5C+%0Ax+%3D++%5Cfrac%7B11%7D%7B56%7D+)
2)
![\frac{2x + 5}{7} + \frac{3x - 1}{2} = x + 1 |* 14](https://tex.z-dn.net/?f=+%5Cfrac%7B2x+%2B+5%7D%7B7%7D+%2B+%5Cfrac%7B3x+-+1%7D%7B2%7D++%3D+x++%2B+1++++++%7C%2A+14)
2(2x + 5) + 7(3x - 1) = 14(x + 1)
4x + 10 + 21x - 7 = 14x + 14
25x + 3 = 14x + 14
25x - 14x = 14 - 3
11x = 11
x = 11 : 11
х = 1
4/15-(y+3/25)=1/25
НАИМЕНЬШИЙ ОБЩИЙ ЗНАМИНАТЕЛЬ= 75
20/75-(y+9/75)=3/75
17/75=y+9/75
y=17/75-9/75
y=6/75
y=0,08
Ответ:
Было бы побольше баллов.....
![\displaystyle ODZ: cosx\neq 0; cos2x\neq0\\\\x\neq \frac{\pi}{2}+\pi n ; x\neq \frac{\pi}{4}+\frac{\pi n}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle+ODZ%3A+cosx%5Cneq+0%3B+cos2x%5Cneq0%5C%5C%5C%5Cx%5Cneq+%5Cfrac%7B%5Cpi%7D%7B2%7D%2B%5Cpi+n+%3B+x%5Cneq+%5Cfrac%7B%5Cpi%7D%7B4%7D%2B%5Cfrac%7B%5Cpi+n%7D%7B2%7D)
рассмотрим два случая
sinx≥0; 2πn≤x≤π+2πn; n∈Z
![\displaystyle \frac{sinx+sin3x}{cosx*cos2x}=\frac{2}{\sqrt{3}}\\\\\frac{2sin2x*cosx}{cosx*cos2x}=\frac{2}{\sqrt{3}}\\\\tg2x=\frac{1}{\sqrt{3}}\\\\2x=\frac{\pi}{6}+\pi n; n\in Z\\\\x=\frac{\pi}{12}+\frac{\pi n}{2}; n\in Z](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Cfrac%7Bsinx%2Bsin3x%7D%7Bcosx%2Acos2x%7D%3D%5Cfrac%7B2%7D%7B%5Csqrt%7B3%7D%7D%5C%5C%5C%5C%5Cfrac%7B2sin2x%2Acosx%7D%7Bcosx%2Acos2x%7D%3D%5Cfrac%7B2%7D%7B%5Csqrt%7B3%7D%7D%5C%5C%5C%5Ctg2x%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D%5C%5C%5C%5C2x%3D%5Cfrac%7B%5Cpi%7D%7B6%7D%2B%5Cpi+n%3B+n%5Cin+Z%5C%5C%5C%5Cx%3D%5Cfrac%7B%5Cpi%7D%7B12%7D%2B%5Cfrac%7B%5Cpi+n%7D%7B2%7D%3B+n%5Cin+Z)
так как sin x≥0 то корни: х=π/12+2πn; x=7π/12+2πn; n∈Z
второй случай sinx<0; π+2πn<x<2π+2πn; n∈Z
![\displaystyle \frac{sin3x-sinx}{cosx*cos2x}=\frac{2}{\sqrt{3}}\\\\\frac{2cos2x*sinx}{cosx*cos2x}=\frac{2}{\sqrt{3}}\\\\tgx=\frac{1}{\sqrt{3}}\\\\x=\frac{\pi }{6}+\pi n; n\in Z](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Cfrac%7Bsin3x-sinx%7D%7Bcosx%2Acos2x%7D%3D%5Cfrac%7B2%7D%7B%5Csqrt%7B3%7D%7D%5C%5C%5C%5C%5Cfrac%7B2cos2x%2Asinx%7D%7Bcosx%2Acos2x%7D%3D%5Cfrac%7B2%7D%7B%5Csqrt%7B3%7D%7D%5C%5C%5C%5Ctgx%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D%5C%5C%5C%5Cx%3D%5Cfrac%7B%5Cpi+%7D%7B6%7D%2B%5Cpi+n%3B+n%5Cin+Z)
так как sinx<0 то корни х= 7π/6+2πn; n∈Z
Выборка корней на промежутке [π/2; 3π/2}
x= 7π/12; 7π/6