Question

Can someone please help me solve and number line this equation?

Answer 1

First, we solve each inequality for x,

1)

`\begin{gathered} 31<-5x-4, \\ 31+4<-5x-4+4, \\ 35<-5x, \\ 35\cdot(1)/(-5)>-5x\cdot(1)/(-5), \\ -7>x\text{.} \\ \end{gathered}`

2)

`\begin{gathered} -5x-4<-59, \\ -5x-4+4<-59+4, \\ -5x<-55, \\ -5x\cdot(1)/(-5)>-55\cdot(1)/(-5), \\ x>11. \end{gathered}`

Then,

`x<-7\text{ or x>11.}`

Answer: The solution for the given system of inequalities is:

`(-\infty,-7)\cup(11,\infty).`

The solution represented on the number line is as follows: