what is the value of x so that the line segment with endpoints A(x,-3) and B(7,-1) is parallel to the line segment with endpoints C(-4,-2) and D(-2,-5)?

C(-4,-2) and D(-2,-5)

The slope between these  =   [ -5 - -2] / [ -2 - -4]   =  [ -5 + 2] / [ -2 + 4]   =  -3/2

So...we're trying to solve this

[-1 - -3] / [7 - x] = -3/2     

[ 2] / [ 7 -x] = -3/2      cross-multiply

2 * 2  = -3 [ 7 - x]     simplify

4 = -21  + 3x       add 21 to both sides

25  = 3x      divide both sides by 3

25 / 3   = x  = 8 + 1/3