How do you graph #-2|x+5|+4=2#?

2 Answers
Aug 11, 2016

The solution to this equation is two possible #x# values which are two points on the #x#-axis.

Explanation:

The solution to this equation is two possible #x# values which we can solve for. The "graph" is more just two points on the #x#-axis or a number-line representing #x#. Let's solve for the points first. Take the original equation and divide both sides by #-2#:

#|x+5|-2=-1#

Then add #2# to both sides

#|x+5| = 1#

Now we see that the quantity inside the absolute value signs must have a magnitude of #1# but can have either sign, therefore:

#x+5=1" "# or #" "x+5=-1#

so the two solutions are

#x = -4, -6#

graphing this we get two points on the #x#-axis

graph{0=(y^2+(x+6)^2-0.02)(y^2+(x+4)^2-0.02) [-10, 10, -5, 5]}

Aug 11, 2016

In support of David's solution I have added a graph showing the actual function.

Explanation:

enter image source here

The values David give are consequential to the point of intersection of #y=-2|x+5|+4# and #y=2#