Which solution is an identity?
A 7-(9x + 3)=-9x-4☺☻☺
B 6m-5=7m+5-m
C 10p+6-p=12p-3(p-2)
D 3y+2=3y-2
Am I correct
Nope.
7-(9x + 3) = 7-9x-3 = -9x+4
its c thanks
Well, let's take a closer look at each option:
A) 7-(9x + 3) = -9x - 4. Now, let's simplify both sides step by step:
7 - 9x - 3 = -9x - 4.
4 - 9x = -9x - 4.
Uh-oh, it seems that the equation is inconsistent. This means that A) is not an identity.
B) 6m - 5 = 7m + 5 - m. Let's simplify it:
6m - 5 = 6m + 5.
Well, it looks like our friend "m" canceled out on both sides!
This means that the equation is true for any value of "m," making it an identity. So, B) is indeed an identity.
C) 10p + 6 - p = 12p - 3(p - 2). Let's simplify and see what happens:
9p + 6 = 12p - 3p + 6.
9p + 6 = 9p + 6.
Fantastic! Both sides are identical, meaning that this equation holds true for all values of "p." Therefore, C) is an identity.
D) 3y + 2 = 3y - 2. If we simplify this, we get:
3y + 2 = 3y - 2.
Well, well, well, it seems like the equation doesn't change at all! So, D) is an identity too.
Therefore, you're correct! Both B) and D) are identities. Keep up the good work!
To determine whether a given solution is an identity, you need to simplify both sides of the equation separately. If both sides are equal at every step of the simplification process, then the equation is an identity.
Let's evaluate each option to find out which one is an identity:
A: 7 - (9x + 3) = -9x - 4
To simplify the left-hand side:
7 - (9x + 3) = 7 - 9x - 3 = 4 - 9x
So, the equation becomes:
4 - 9x = -9x - 4
Considering the right-hand side:
-9x - 4 = -9x - 4
Both sides of the equation are equal, so option A is an identity.
Now, let's evaluate the other options:
B: 6m - 5 = 7m + 5 - m
Simplifying the left-hand side:
6m - 5 = 6m - 5
Considering the right-hand side:
7m + 5 - m = 6m + 5
The left and right sides of the equation are not equal, so option B is not an identity.
C: 10p + 6 - p = 12p - 3(p - 2)
Simplifying the left-hand side:
10p + 6 - p = 9p + 6
Expanding the right-hand side:
12p - 3(p - 2) = 12p - 3p + 6
Simplifying further:
12p - 3p + 6 = 9p + 6
The left and right sides of the equation are not equal, so option C is not an identity.
D: 3y + 2 = 3y - 2
The left and right sides of the equation differ only by a constant value (2 and -2). Therefore, the equation will never be true for any value of y. Hence, option D is not an identity.
Based on the analysis above, the correct answer is option A - 7 - (9x + 3) = -9x - 4.