Question

O EQUATIONS AND INEQUALITIESSolving a compound linear inequality: Interval notation

Answer 1

Step-by-step explanation

For the given compound inequality

`\begin{gathered} 3x+6\ge24 \\ or \\ 2x-6>0 \end{gathered}`

We will solve the inequalities independently so that

`\begin{gathered} 3x+6\ge24 \\ 3x\ge24-6 \\ 3x\ge18 \\ \\ x\ge(18)/(3) \\ \\ x\ge6 \end{gathered}`

Also

`\begin{gathered} 2x-6>0 \\ 2x>6 \\ \\ x>(6)/(2) \\ \\ x>3 \end{gathered}`

So, we have

`x\ge6\text{ or x}>3`

Combining the two rs

Thus, the answer will be

`\begin{bmatrix}\mathrm{Solution:}\:&\:x>3\:\\ \:\mathrm{Interval\:Notation:}&\:\left(3,\:\infty \:\right)\end{bmatrix}`