Question

The solution set of which inequality is represented by the number line below

Answer 1

Let's solve the last inequality

`-2x+5<-3`

First, we subtract 5 from each side

`\begin{gathered} -2x+5-5<-3-5 \\ -2x<-8 \end{gathered}`

Then, we divide the inequality by -2

`\begin{gathered} (-2x)/(-2)>-(8)/(-2) \\ x>4 \end{gathered}`

The solution to this inequality is all the real numbers greater than 4.

`\begin{gathered} 4x+6>22 \\ 4x>22-6 \\ x>(16)/(4) \\ x>4 \end{gathered}`

`\begin{gathered} 6x-7\leq17 \\ 6x\leq17+7 \\ x\leq(24)/(6) \\ x\leq4 \end{gathered}`