How many solutions does the equation have? 6-a = 1/3(9a-18)
a. one solution
b. infinite solutions
c. no solution

6 - a =  (9a - 18)

First, simplify  to  / Your problem should look like: 
Second, multiply both sides by 3. / Your problem should look like: 
Third, expand. / Your problem should look like: 
Fourth, add 3a to both sides. / Your problem should look like: 
Fifth, simplify 9a - 18 + 3a to 12a - 18. / Your problem should look like: 
Sixth, add 18 to both sides. / Your problem should look like: 
Seventh, add 18 + 18 to get 36. / Your problem should look like: 
Eighth, divide both sides by 12. / Your problem should look like: 
Ninth, since 3 goes into 12 to get 36, simplify  to 3. / Your problem should look like: 
Tenth, switch sides. / Your problem should look like: 

 a = 3 (one solution)

Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.