Please solve, picture attached below!
Thanks!

x = -1 or 15

Step-by-step explanation:

If the absolute value equals 8, the value of x - 7 can either be -8 or 8.

We first solve for when it is equal to -8:

x - 7 = -8

We can add 7 to both sides:

x = -1

Now we can solve for when it's equal to 8:

x - 7 = 8

We can add 7 to both sides:

x = 15

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.