Question

How many solutions does the equation have? 6-a = 1/3(9a-18)

a. one solution
b. infinite solutions
c. no solution

Answer 1

6 - a =
`(1)/(3)` (9a - 18)

First, simplify
`(1)/(3) (9a - 18)` to
`(9a-18)/(3)` / Your problem should look like:
`6 - a = (9a - 18)/(3)`
Second, multiply both sides by 3. / Your problem should look like:
`18 - 3a = 9(a - 2)`
Third, expand. / Your problem should look like:
`18 - 3a = 9a - 18`
Fourth, add 3a to both sides. / Your problem should look like:
`18 = 9a - 18 + 3a`
Fifth, simplify 9a - 18 + 3a to 12a - 18. / Your problem should look like:
`18 = 12a - 18`
Sixth, add 18 to both sides. / Your problem should look like:
`18 + 18 = 12a`
Seventh, add 18 + 18 to get 36. / Your problem should look like:
`36 = 12a`
Eighth, divide both sides by 12. / Your problem should look like:
`(36)/(12) = a`
Ninth, since 3 goes into 12 to get 36, simplify
`(36)/(12)` to 3. / Your problem should look like:
`3 = a`
Tenth, switch sides. / Your problem should look like:
`a = 3`

Answer: a = 3 (one solution)