Question

I need help with #12. I have to show work too.

Answer 1

Answer: SR is 69 units long.

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Explanation/Work Shown:

SR is the distance from R to S (or S to R; order doesn't matter). In other words, it's the length of segment SR. In this case, SR = 7x-8 for now. Your teacher wants you to find a numeric value for SR. To do that, we need to find x first.

ST is a similar story: it's the length of segment ST. In this case, ST is the algebraic expression 3x-5. 
Finally, RT = 8x+9

So far we have these three equations:
SR = 7x-8
ST = 3x-5
RT = 8x+9

Because SR and ST combine to form RT (and because S is on line RT), this means we can say
SR + ST = RT
by the segment addition postulate

Let's plug in the equations found earlier to get...
SR + ST = RT
(7x-8) + ST = RT ... replace SR with 7x-8
(7x-8) + (3x-5) = RT ... replace ST with 3x-5
(7x-8) + (3x-5) = 8x+9 ... replace RT with 8x+9

Now let's solve for x
(7x-8) + (3x-5) = 8x+9
7x-8 + 3x-5 = 8x+9
(7x+3x)+(-8-5) = 8x+9
10x-13 = 8x+9
10x-13+13 = 8x+9+13 ... add 13 to both sides
10x = 8x+22
10x-8x = 8x+22-8x ... subtrat 8x from both sides
2x = 22
2x/2 = 22/2 ... divide both sides by 2
x = 11

Now that we know x, we can find the length of SR
SR = 7x-8
SR = 7*x-8
SR = 7*11-8 ... replace x with 11 (since x = 11)
SR = 77-8
SR = 69