Given the function
[tex]g(x)=-|2x+4|+3[/tex]The expressions are equivalent if they show the same result as the original one.
A.
[tex]g(x)=-(2x+4)+3[/tex]Since the terms held by the | | are positive, one solving the multiplication by -1 they will be negative with or without the module. This means that this expression is equivalent. (Alsmos the same just changed the module lines by parenthesis)
B.
[tex]g(x)\left\{ \begin{aligned}2x+7,\text{ x<-2} \\ 1-2x-1,\text{ x2-2}\end{aligned}\right.[/tex]C.
[tex]g(x)\left\{ \begin{aligned}-2x-1,x<-2 \\ 2x+7,x2-2\end{aligned}\right.[/tex]D.
[tex]g(x)\left\{ \begin{aligned}-(2x+4)+3,x<0 \\ (2x+3)+3,x-20\end{aligned}\right.[/tex]For the expressions that you posted, only A is equivalent.
