can you help me with this. d don't get it at all :(
let n be the number used for the given number puzzle. use algebra to show how the puzzle works.
1. pick a number
2. subtract 9
3. multiply by 6
4. divide by 3
5. add 18
6. subtract twice your original number
You will always get zero
Here is how to follow the first six steps. Try finishing it yourself.
Call the number you pick x.
x-9
6(x-9)
6(x-9)/3 = 2(x-3)
2(x-9)+18
subrtact 2x from that
i am still confused on the last step
Sure, I can help you with that!
Let's start by assuming that the original number you picked is represented by the variable "n".
Step 1: Pick a number
Since you picked a number, we have the value of "n" established.
Step 2: Subtract 9
Now, we subtract 9 from the chosen number. This can be represented as "n - 9".
Step 3: Multiply by 6
Next, we multiply the result from step 2 by 6. This can be represented as "6*(n - 9)".
Step 4: Divide by 3
After that, we divide the result from step 3 by 3. This can be represented as "(6*(n - 9))/3".
Step 5: Add 18
Following that, we add 18 to the result obtained in step 4. This can be represented as "(6*(n - 9))/3 + 18".
Step 6: Subtract twice your original number
Finally, we subtract twice your original number which is represented as "2n". So, the final expression becomes "(6*(n - 9))/3 + 18 - 2n".
The goal is to show that this expression always equals zero, regardless of the original number picked (n). To prove this, we need to simplify the expression and show that it simplifies to zero.
Let's simplify the expression step by step:
(6*(n - 9))/3 + 18 - 2n
(2*(n - 9)) + 18 - 2n (cancel out the 3 in the numerator and denominator)
2n - 18 + 18 - 2n (distribute the 2 into the parentheses)
2n - 2n - 18 + 18 (combine like terms)
0 (cancel out the like terms -2n and 2n, and -18 + 18 equals zero)
As you can see, the expression simplifies to zero regardless of the original number picked. Therefore, following the given steps of the puzzle will always result in zero.