Offering points!

the numbers 1 through 8 are to be placed in the circles in the diagram shown such that the sum of the numbers on each side of the figure is 15. find the values of x, y, and z. then copy the diagram on a piece of paper and fill in each circle with the appropriate number. be sure to show all your work. upload the finished problem below.

note: x satisfies –4(x – 2) = –4,

y satisfies 9 + 2(y – 3) = 3(y – 2) + 1,

and z satisfies z/3+1/2=5/2.

Step-by-step explanation:

Solve for x

- 4 (x - 2) = - 4           There are a a couple of ways of doing this. Divide by - 4

-4 (x - 2)/-4 = - 4/-4   Combine

x - 2 = 1                     Add 2

x = 3

Solve for y

9 + 2(y - 3) = 3(y - 2) + 1        Remove the brackets on both sides.

9 + 2y - 6 = 3y - 6 + 1           Combine

9 - 6 + 2y = 3y - 5                

3 + 2y = 3y - 5                      Add 5

3 + 5 + 2y = 3y                      Subtract 2y

8 + 2y - 2y = 3y - 2y

8 = y

Solve for z

z/3 + 1/2 = 5/2                       Subtract 1/2 from both sides.

z/3 + 1/2 - 1/2 = 5/2 - 1/2       Combine

z/3 = 4/2

z/3 = 2                                   Multiply by 3

z/3*3 = 2*3

z = 6

So far what you have is

3

==

8 ||  6

== must = 4 because 3 + 8 + 4 = 15

||  must =  1 because 8 + 6 + 1 = 15

You have 3 numbers left to place 5,7,2

The right hand upper corner = 7.

I'll leave you to place the 5 and 2

-2x + 7 = 7

subtract 7 from both sides.

-2x = 0

divide both sides by -2.

x = 0

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step-by-step explanation: