Question

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

Answer 1

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]}

Answer 2

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

Explanation:

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