Question

Which compound inequality is equivalent to lax-bl > C for all real numbers a, b, and c, where c_>o?-Cc-c> ax-b>cax-b>-c or ax->Cax-b<-c or ax-b>c

Answer 1

In general,

`\begin{gathered} |a|>b,b\geq0 \\ then, \\ a<-b \\ or \\ a>b \end{gathered}`

Applying this rule to our inequality, we have:

`\begin{gathered} |ax-b|>c \\ \text{then,} \\ ax-b<-c------\text{Inequality}1 \\ or \\ ax-b>c-------\text{Inequality}2 \end{gathered}`

From the answer choices, the last answer choice is correct!

Answer
`\begin{gathered} ax-b<-c \\ or \\ ax-b>c \end{gathered}`