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Absolute value inequalities. 10-4|9y-10|<-94

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et762572

Answer: [tex]\begin{bmatrix}\mathrm{Solution:}\:&\:y<-\frac{16}{9}\quad \mathrm{or}\quad \:y>4\:\\ \:\mathrm{Decimal:}&\:y<-1.77777\dots \quad \mathrm{or}\quad \:y>4\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-\frac{16}{9}\right)\cup \left(4,\:\infty \:\right)\end{bmatrix}[/tex]

Step-by-step explanation:

[tex]10-4\left|9y-10\right|<-94[/tex]

[tex]10-4\left|9y-10\right|-10<-94-10[/tex]

[tex]-4\left|9y-10\right|<-104[/tex]

[tex]\left(-4\left|9y-10\right|\right)\left(-1\right)>\left(-104\right)\left(-1\right)[/tex]

[tex]4\left|9y-10\right|>104[/tex]

[tex]\frac{4\left|9y-10\right|}{4}>\frac{104}{4}[/tex]

[tex]\left|9y-10\right|>26[/tex]

[tex]9y-10<-26\quad \mathrm{or}\quad \:9y-10>26[/tex]

[tex]y<-\frac{16}{9}\quad \mathrm{or}\quad \:y>4[/tex]

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