Question

How to solve compound inequalities?

I have been stuck on these for awhile now and have watched a few videos but still dont understand..

|x|>9

|b+6|<(with a line under it)5

|y+6|>13

|11-2b|-6>11

I dont want answers for all, but would love for someone to explain so i can understand and do it on my own.

Answer 1

So are those 1 whole problem or 4 separate problems?

Answer 2

\(\bf |x|>9\implies
\begin{cases}
+(x)>9\\ \quad \\
\bf -(x)>9
\end{cases}\\\\ \quad \\

|b+6|\le 5\implies
\begin{cases}
+(b+6)\le 5\\ \quad \\
\bf -(b+6)\le 5
\end{cases}\\\\ \quad \\

|y+6|>13\implies
\begin{cases}
+(y+6)>13\\ \quad \\
\bf -(y+6)>13
\end{cases}\\\\ \quad \\

|11-2b|-6>11\implies |11-2b| > 11+6\implies |11-2b| > 17\\ \quad \\
\bf |11-2b| > 17\implies
\begin{cases}
+(11-2b)>17\\ \quad \\
\bf -(11-2b)>17
\end{cases}\)

each absolute value expression, will give you 2 values for "x", 1 for each scenario