We are given the following absolute value equation.
|x+2|=4
We are asked to match the absolute value equation with one of the given graphs without solving the equation. Let's start by recalling that if we have two points on a number line, we can use the halfway point between the points and the distance from each point to the halfway point to write an absolute value equation.
|x- halfway point|= distance from halfway point
Notice that the left-hand side of the equation is in the form |x-a|. Keeping that in mind, we can rewrite our equation. Let's do it!
|x+2|=4 ⇔ |x-( - 2)|= 4
Now, we can determine the halfway point as - 2 and the distance from the halfway point as 4.
We can see that this number line corresponds with option B. This means that the graph from option B represents the given absolute value equation.
