Solve 7x - 2(x + 1) = 6x + 14

Answer

Step-by-step explanation:

First Simplify  7x-2x-27x−2x−2  to  5x-25x−2.

7x - 2(x + 1) = 6x + 14

second Subtract 5xfrom both sides.

5x−2=6x+14

third  Simplify  6x+14-5 to  x+14

−2=6x+14−5x

fourth Subtract 14 from both sides.

−2=x+14

fifth Simplify  -2-14 to -16

−2−14=x

six  Switch sides.              7 x= -16  

−16=x

x=−16

Step-by-step explanation:

7x−2(x+1)=6x+14

Use the distributive property to multiply −2 by x+1.

7x−2x−2=6x+14

Combine 7x and −2x to get 5x.

5x−2=6x+14

Subtract 6x from both sides.

5x−2−6x=14

Combine 5x and −6x to get −x.

−x−2=14

Add 2 to both sides.

−x=14+2

Add 14 and 2 to get 16.

−x=16

Multiply both sides by −1.

x=−16

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

michael scott & dwight schrute

step-by-step explanation:

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