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

1 Answer
Jan 13, 2018

Answer:

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]}