Question

Find the solution set of the equation: (See below)

Answer 1

\[|\frac{ x-7 }{ 2 }|+8=8\]

Answer 2

take 8 from both sides

Answer 3

there is only one solution

Answer 4

So how would I get rid of the fraction inside of the brackets so that I could solve for x?

Answer 5

\[\left|\frac{x-7}{2}\right|=0\]

Answer 6

Right I got that. Sow how would that be expressed in interval notation if left like that?

Answer 7

for what values of x is the equation satisfied ?

Answer 8

dont leave it like that the only solution is x=somenumber

Answer 9

\[\left|\frac{x-7}{2}\right|=0\]\[\frac{\left|x-7\right|}{\left|2\right|}=0\]\[\frac{\left|x-7\right|}{2}=0\]\[\left|x-7\right|=0\]

Answer 10

How did you cancel the 2?

Answer 11

\[\frac{\left|x-7\right|}{2}=0\]
\[2\times\frac{\left|x-7\right|}{2}=2\times0\]
\[\left|x-7\right|=0\]

Answer 12

So you just cross canceled by multiplying both sides by 2?

Answer 13

exactly

Answer 14

So then I take that problem and come up with my solution set of (0,7)?

Answer 15

I got it {7}. Thanks!