Why did you square 2x?
(2x + 3) - (x - 6)
2x - x = x
3 + 6 = 9
(2x + 3) - (x - 6) = x + 9
I rewrote this as (97 + 3) + 13 since the associative property is about changing the grouping. The answer in the back of the book says 97 + (3 + 13) -- the same as the original problem.
2. Use the distributive property to simplify (2x + 3) - (x - 6)
I got -2x squared + 9x + 18 but the answer in the back of the book says x + 9
Could you explain where I went wrong on this problem please?
(2x + 3) - (x - 6)
2x - x = x
3 + 6 = 9
(2x + 3) - (x - 6) = x + 9
What about the first question?
You're welcome.
Here's a step-by-step explanation:
Original expression: 97 + (3 + 13)
Using the associative property, you can change the grouping:
(97 + 3) + 13
Simplifying inside the parentheses:
100 + 13
Adding the remaining numbers:
113
So, both 97 + (3 + 13) and (97 + 3) + 13 are equivalent and give the same result of 113.
Now let's move on to the second problem:
Expression: (2x + 3) - (x - 6)
To simplify this using the distributive property, we need to distribute the subtraction sign to both terms inside the parentheses:
Expression after distribution: (2x + 3) - x + 6
Now, let's simplify further by combining like terms:
2x - x = x
3 + 6 = 9
Putting it all together: x + 9
Therefore, the simplified form of (2x + 3) - (x - 6) is x + 9. It seems you made an error when combining the terms in the second step, which led to the incorrect answer -2x squared + 9x + 18. Remember to carefully combine like terms and perform the necessary operations accurately.