functions (1 Viewer)

[purpletree]

determine for what value of c the equation |2x-1|=x+c has exactly two solutions

 

[purpletree]

bump

 

[Manroop]

solve the equation and you should get two equation involving x and c. Solve simultaneously to get value of c.

 

[Carrotsticks]

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.