How do I express this in algebraic form? And could you please explain how you came up with the expression?
"Come up with a number. Add 3 to it. Muliply by 1 more than the original number. Subtract 3. Divide by the original number. Subtract 4. You should get the original number.
How it works: x is the original number. Add 3 to x to get (x+3). Multiply by (x+1) to get x² + 4x + 3. Subtract 3 to get x² + 4x, which factorises to x(x+4). Dividing by the original number, x, gives x + 4, and subtracting 4 gives the original number, x."
Is (x^2+4x/x)-4 correct?
Come up with a number: x
Add 3 to it : x+3
Muliply by 1 more than the original number : (x+3)(x+1)
Subtract 3 : (x+3)(x+1) - 3
Divide by the original number : [(x+3)(x+1) - 3]/x
Subtract 4 : [(x+3)(x+1) - 3]/x - 4
[(x+3)(x+1) - 3]/x - 4
= (x^2 + 4x +3 - 3)/x - 4
= (x^2 + 4x)/x - 4
= x + 4 - 4
= x
Notice the long expression follows the actual wording.
Your answer of (x^2+4x/x)-4 needs brackets like this:
(x^2+4x)/x - 4 or else only the 4x is divided by x
To express the given process in algebraic form, let's break it down step by step:
1. "Come up with a number": Let's call this number 'x'.
2. "Add 3 to it": This can be written as (x + 3).
3. "Multiply by 1 more than the original number": The original number is 'x', and 1 more than that is (x + 1). So, we multiply (x + 3) by (x + 1), resulting in (x + 3)(x + 1), which can be further simplified as x² + 4x + 3 using the distributive property.
4. "Subtract 3": Subtracting 3 from x² + 4x + 3 gives x² + 4x (since -3 - 3 = -6).
5. "Divide by the original number": We divide x² + 4x by x, resulting in x(x + 4). Notice that we can divide each term of x² + 4x by x, giving x + 4.
6. "Subtract 4": Finally, subtracting 4 from x + 4 gives the original number x.
So, the algebraic expression representing the given process is:
x = x
Let's recap the steps:
- Original number: x
- Add 3: (x + 3)
- Multiply by 1 more than the original number: (x + 3)(x + 1) = x² + 4x + 3
- Subtract 3: x² + 4x + 3 - 3 = x² + 4x
- Divide by the original number: (x² + 4x) / x = x + 4
- Subtract 4: x + 4 - 4 = x
Hence, we end up with x = x, demonstrating that the process brings us back to the original number.