Solve the inequality. |4x + 2| < 26 –7 > x > 6 –32 < x < 20 –6 < x < 6 –7 < x < 6

-7< x < 6

Step-by-step explanation:

|4x + 2| < 26

The absolute value has a positive and a negative.  Remember to flip the inequality when taking the negative

4x+2 < 26       and 4x+2 > -26

Subtract 2 from each side

4x+2-2 < 26 -2   and 4x+2 > -26-2

4x < 24              and 4x > -28

Divide by 4

4x/4 < 24                  4x/4 >-28/4

x <6          and                    x> -7

-7< x < 6

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.

-2x-4

step-by-step explanation: