Solve |2x - 2| < 8 {x|-3 < x < 5}
{x|x < -3 or x > 5}
{x|-5 < x < 3}

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |2x-2|

For the Negative case we'll use -(2x-2)

For the Positive case we'll use (2x-2)

-(2x-2) < 8

Multiply

-2x+2 < 8

Rearrange and Add up

-2x < 6

Divide both sides by 2

-x < 3

Multiply both sides by (-1)

Remember to flip the inequality sign

x > -3

Which is the solution for the Negative Case

(2x-2) < 8

Rearrange and Add up

2x < 10

Divide both sides by 2

x < 5

Which is the solution for the Positive Case

One solution was found :

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.

804.75

step-by-step explanation: