purpletree
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determine for what value of c the equation |2x-1|=x+c has exactly two solutions
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purpletree
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Carrotsticks
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Just do it graphically.
By drawing the sketch of y=|2x-1| and y=x-0.5, we see that it intersects only once (at the bottom of the 'V') so quite clearly any larger values of C than -0.5 will yield two points of intersections...
Alternatively, you could square both sides, make a quadratic in terms of X, then let the discriminant be > 0.
You will easily see that the region is c > -0.5.
By drawing the sketch of y=|2x-1| and y=x-0.5, we see that it intersects only once (at the bottom of the 'V') so quite clearly any larger values of C than -0.5 will yield two points of intersections...
Alternatively, you could square both sides, make a quadratic in terms of X, then let the discriminant be > 0.
You will easily see that the region is c > -0.5.