We have the points A(2,-2) B(1,1) C(1,4) and D(x,5) and we need to find x if AB and CD are parallel.

The slope of AB is (1+2)/(1-2) = 3/-1 = -3

The slope of CD is (5-4)/(x - 1) = 1/(x - 1)

For parallel lines the slope is the same

=> 1/(x - 1) = -3

=> 1 = -3x + 3

=> 3x = 2

=> x = 2/3

**The required value of x = 2/3**

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