Question

How do you solve | x - 3 | = x + 1 graphically?

Answer 1

See explanation.

Explanation:

Look at the equation as two functions: `y=abs(x-3)` and `y=x+1`.

To graph `y=abs(x-3)` we know the the vertex is at `(3,0)`. The slope to the right of the vertex is 1 and the slope to the right of the vertex is `-1`. The graph is piecewise linear. So graph `y=-(x-3)` for `x<=3` and `y=x-3` for `x>3`.

The graph of `y=x+1` is a linear function with a `y`-intercept of `(0,1)` and `x`-intercept of `(-1,0)`.

If you graph carefully enough you can see that the only intersection point is at `(1,2)`, where the left branch of the absolute value, `y=-(x-3)` intersects the linear function, `y=x+1`.

Here's the graph.
graph{(y-abs(x-3))(y-x-1)=0 [-7.83, 12.17, -2.6, 7.4]}