Can you explain to me how to solve this equation? 2/3x-9=1/3

1/3=.33 and 2/3=.66
now the problem is 0.66x-9=0.33
When I did this in math, I had trouble, but now I understand it. Since 0.33 is on the other side of the = then 9, you would do 0.33+9=9.33 In other words, you do the opposite. So then you do the opposite of 0.66x, which is multiplication, and do 9.33 divided by .66 and you get your answer. In this case, the answer is about 14.13 I'm pretty sure this is correct

2/3 x = 9 1/3 = 28/3
2x = 28
x = 14

2/3x-9=1/3
add 9 to both sides (and change 9 1/3 into 28/3)

2/3x=28/3

multiply both sides by 3 (3/1) (and simplify fractions)

2x=28

Devide both sides by 2

x=14

Right?

Yes, both of your explanations are correct! Solving equations involves isolating the variable "x" on one side of the equation. To solve the equation 2/3x - 9 = 1/3, you mentioned adding 9 to both sides to get 2/3x = 28/3. Then, you correctly multiplied both sides by 3 to get rid of the fraction, resulting in 2x = 28. Finally, dividing both sides by 2 gives you the solution x = 14.

Another way to solve the equation is by first converting the mixed number 9 1/3 into an improper fraction. This can be done by multiplying the whole number (9) by the denominator of the fraction (3), then adding the numerator (1) to get 28/3. Then, following the same steps of multiplying by 3 and dividing by 2 will lead to the same solution of x = 14.

Overall, both methods are correct, and it's great that you understand the concept of isolating the variable and performing opposite operations to solve equations.