What values of $c$ in the equation $|2x+1|=x+c$ give exactly two solutions?

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What values of $c$ in the equation $|2x+1|=x+c$ give exactly two solutions?

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Answer 1 · 2018-02-11T12:24:14

See below.

Explanation:

This problem can be easily solved graphically.

Below we can see in blue the function $y = abs(2x+1)$ and in red the function $y = x+c$ for $c = 1/2$ It is evident that for $c > 1/2$ we have two intersections so the answer is $c gt 1/2$

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What values of $c$ in the equation $|2x+1|=x+c$ give exactly two solutions?

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What values of $c$ in the equation $|2x+1|=x+c$ give exactly two solutions?