Question

Lxl +20<11Are all real numbers solutions?

Answer 1

No solution

Step-by-step explanation:

We were given the inequality:

`|x|+20<11`

We will proceed to solve for the unknown variable "x" to see if all real numbers are solutions as shown below:

`\begin{gathered} |x|+20<11 \\ \text{Subtract ''20'' from both sides, we have:} \\ |x|+20-20<11-20 \\ |x|<-9 \\ when\colon x=-10 \\ |-10|\Rightarrow10 \\ |-10|<-9\Rightarrow10<-9 \\ 10<-9\mleft(FALSE\mright?_{}) \\ when\colon x=-50 \\ |-50|\Rightarrow50 \\ |-50|<-9\Rightarrow50<-9 \\ 50<-9(FALSE) \\ \\ |x|<-9 \\ \therefore\text{ This means this inequality has no solution} \end{gathered}`

Therefore, this inequality has no solution (all real numbers are not solutions)