Question

Solve the compound inequality3x+4 > 13 or 4x4 <--24Graph the solution on the number line,

Answer 1

The given inequalities are

`\begin{gathered} 3x+4>13 \\ 4x-4<-24 \end{gathered}`

Let us start by 12t inequality,

Subtract 4 from each side

`\begin{gathered} 3x+4-4>13-4 \\ 3x>9 \end{gathered}`

Divide each side by 3

`\begin{gathered} (3x)/(3)>(9)/(3) \\ x>3 \end{gathered}`

For the 2nd inequality

Add 4 to each side

`\begin{gathered} 4x-4+4<-24+4 \\ 4x<-20 \end{gathered}`

Divide each side by 4

`\begin{gathered} (4x)/(4)<(-20)/(4) \\ x<-5 \end{gathered}`

We will represent these solutions on the number line

The solution of the compound inequality is

x < -5 and x > 3

You have to end the lines with arrows