Question

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

Answer 1

Answer:
`\begin{bmatrix}\mathrm{Solution:}\:&\:y<-(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 \:,\:-(16)/(9)\right)\cup \left(4,\:\infty \:\right)\end{bmatrix}`

Explanation:

`10-4\left|9y-10\right|<-94`

`10-4\left|9y-10\right|-10<-94-10`

`-4\left|9y-10\right|<-104`

`\left(-4\left|9y-10\right|\right)\left(-1\right)>\left(-104\right)\left(-1\right)`

`4\left|9y-10\right|>104`

`(4\left|9y-10\right|)/(4)>(104)/(4)`

`\left|9y-10\right|>26`

`9y-10<-26\quad \mathrm{or}\quad \:9y-10>26`

`y<-(16)/(9)\quad \mathrm{or}\quad \:y>4`