Question

Let f(x) = 2x + 4 and g(x)= 3x - 3. Find all values of x for which f(x) 6 and g(x) > 18.The solution set in interval notation is

Answer 1

The given functions are,

$\begin{gathered} f(x)=2x+4 \\ g(x)=3x-3 \end{gathered}$

The given inequality is,

$\begin{gathered} f(x)\ge6 \\ g(x)>18. \end{gathered}$

The given inequality can be solved as,

$\begin{gathered} 2x+4\ge6 \\ \Rightarrow2x\ge2 \\ \Rightarrow x\ge1 \end{gathered}$$\begin{gathered} 3x-3>18 \\ 3x>21 \\ x>7 \end{gathered}$

The solution set using the intersection is,

$x\in(7,\infty)$