Solve the problem c.
s7 is the sum to the arithmetic series of 7 terms.
i've been trying to do it, but i get to the point when the number of terms is 25.6, which is obviously incorrect.

Sure.

The common difference is 1/3

d = 8/15 - 1/5 = 8/15 - 3/15 = 5/15 = 1/3

d = 13/15 - 8/15 = 5/15 = 1/3

So the seventh term is

S_n = S_1 + (n-1)d

S_7 = (1/5)  + 6(1/3) = 11/5

The sum is the average of the first and last times the number of elements

(1/2)(1/5 + 11/5)(7) = 7(6/5) = 42/5 = 8.4

42/5

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.