Question

Given the function f(x) = 2|x + 6| – 4, for what values of x is f(x) = 6?

Answer 1

`\bf f(x)=2|x+6|-4\implies \stackrel{f(x)}{6}=2|x+6|-4\implies 6+4=2|x+6| \\\\\\ \cfrac{10}{2}=|x+6|\impliedby \begin{array}{llll} \textit{keep in mind an absolute value}\\ \textit{expression is in effect a piece-wise} \end{array} \\\\\\ 5=|x+6|\implies \begin{cases} 5=+(x+6)\\ 5=-(x+6) \end{cases}\implies \begin{cases} 5=x+6\implies &-1=x\\ 5=-x-6\implies &x=-11 \end{cases}`