i think of a number then i multiply it by 2, then i add 1, then divide the answer by 3,then i add 2, my final answer is equal to the number i thought of at the beginning

Question

Qa. write down the algebraic equation that represents the problem.

Qb. solve your equation to find the number he or she started with.

Answer 1

(2x +1)/3 + 2 = x

multiply both sides by 3

2x+1 + 6 = 3x

3x-2x = 6+1

x = 7

Answer 2

Let (x) be the number you thought of. What you've done is, according to your description:

First, multiplied by 2, so now we have 2x.

Then, add 1. So now we have 2x+1

Then, you divided by 3, so now we have (2x+1) / 3

Finally, you add 2, and now you have ((2x+1 ))/ 3) + 2

We are told this is equal to the original number, which means we are trying to solve:

((2x+1 ))/ 3) + 2 = x

We can solve this by sort of "undoing" the stuff on the left. Here's how I would do it:

1. ((2x+1 ))/ 3) + 2 = x
2. ((2x+1 ))/ 3) = x-2
3. 2x+1 = 3x-6
4. 1 = x - 6
5. x = 7

Now we can check this by seeing if it works. I think of 7, I multiply by 2, so now I have 14. I add 1, so now I have 15. I divide by 3, so now I have 5. I add 2, so now I have 7. I AM thinking of the number I thought of originally, our solution works :)