Explanation
For the given compound inequality
[tex]\begin{gathered} 3x+6\ge24 \\ or \\ 2x-6>0 \end{gathered}[/tex]
We will solve the inequalities independently so that
[tex]\begin{gathered} 3x+6\ge24 \\ 3x\ge24-6 \\ 3x\ge18 \\ \\ x\ge\frac{18}{3} \\ \\ x\ge6 \end{gathered}[/tex]
Also
[tex]\begin{gathered} 2x-6>0 \\ 2x>6 \\ \\ x>\frac{6}{2} \\ \\ x>3 \end{gathered}[/tex]
So, we have
[tex]x\ge6\text{ or x}>3[/tex]
Combining the two rs
Thus, the answer will be
[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:x>3\:\\ \:\mathrm{Interval\:Notation:}&\:\left(3,\:\infty \:\right)\end{bmatrix}[/tex]
