Solve the equation and show all work. 4|x + 1/3| = 20 i'm kind of stuck hhh

Absolute value is a function that takes some number and outputs the size of that number, regardless of the sign. By definition, [tex]|x|=x[/tex] if [tex]x\ge0[/tex], and [tex]|x|=-x[/tex] if [tex]x<0[/tex].For example,|2| = 2 because the input 2 is positive, so the input is unchanged;|-3| = -(-3) = 3 because the input -3 is negative, so the sign is switched.What this means for this problem is that there are two cases to consider:If [tex]x+\frac13\ge0[/tex], then [tex]\left|x+\frac13\right|=x+\frac13[/tex], so that[tex]4\left(x+\dfrac13\right)=20\implies x+\dfrac13=5\implies\boxed{x=\dfrac{14}3}[/tex]On the other hand, if [tex]x+\frac13<0[/tex], then [tex]\left|x+\frac13\right|=-\left(x+\frac13\right)[/tex], so[tex]-4\left(x+\dfrac13\right)=20\implies x+\dfrac13=-5\implies\boxed{x=-\dfrac{16}3}[/tex]