Ответ:
[tex]2\frac{5}{11};\; \; -3[/tex]
Решение:
5у+2|3-4у|=2у+21
2|3-4y| = 2y+21-5y
2|3-4y| = 21-3y
|4y-3| = (21-3y)/2
|4y-3| = 10,5-1,5y
4y-3 = 10,5-1,5y и 4y-3= 1,5y-10,5
4y+1,5y=10,5+3 4y-1,5y=3-10,5
5,5y=13,5 2,5y=-7,5
y=13,5/5,5 y=-7,5:2,5
y=27/11 y₂= -3
y₁ = 2 5/11
[tex]\displaystyle 5y+2|3-4y|=2y+21\\5y+2|3-4y|-2y=21\\3y+2|3-4y|=21\\\\3y+2(3-4y)=21,3-4y\geq 0 \rightarrow y=-3,y \leq \frac{3}{4} \rightarrow y=-3\\ \\3y+2(-(3-4y))=21,3-4y < 0 \rightarrow y=\frac{27}{11},y > \frac{3}{4} \rightarrow y=\frac{27}{11}\\ \\y_1=-3,y_2=\frac{27}{11}[/tex]
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Verified answer
Ответ:
[tex]2\frac{5}{11};\; \; -3[/tex]
Решение:
5у+2|3-4у|=2у+21
2|3-4y| = 2y+21-5y
2|3-4y| = 21-3y
|4y-3| = (21-3y)/2
|4y-3| = 10,5-1,5y
4y-3 = 10,5-1,5y и 4y-3= 1,5y-10,5
4y+1,5y=10,5+3 4y-1,5y=3-10,5
5,5y=13,5 2,5y=-7,5
y=13,5/5,5 y=-7,5:2,5
y=27/11 y₂= -3
y₁ = 2 5/11
[tex]\displaystyle 5y+2|3-4y|=2y+21\\5y+2|3-4y|-2y=21\\3y+2|3-4y|=21\\\\3y+2(3-4y)=21,3-4y\geq 0 \rightarrow y=-3,y \leq \frac{3}{4} \rightarrow y=-3\\ \\3y+2(-(3-4y))=21,3-4y < 0 \rightarrow y=\frac{27}{11},y > \frac{3}{4} \rightarrow y=\frac{27}{11}\\ \\y_1=-3,y_2=\frac{27}{11}[/tex]