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

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

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Answer 1 · 2018-01-13T10:53:19

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]}

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

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