2. Solve the equation:
3 ( x -7 ) - x = 2x - 21
A) 7
B) -2
C) Infinitely many solutions
D) No solution
3. Which equation is an identity?
A) 8-(5x+2)=-5x-6
B) 7z+10-z=8z-2(z-5)
C) 8m-4=5m+8-m
D) 6y+5=6y-5
I think
C
B
#2 correct
#3 correct
looks good
Well, let's see if I can solve these equations with my humor powers!
For the first equation, let's simplify it step by step:
3(x - 7) - x = 2x - 21
First, let's distribute the 3 to both terms inside the parentheses:
3x - 21 - x = 2x - 21
Now, let's combine like terms on both sides of the equation:
2x - 21 = 2x - 21
Hmm, it seems like we are getting the same expression on both sides. This means the equation has infinitely many solutions!
So for the first question, the answer is C) Infinitely many solutions!
Now, onto the second question!
Let's take a look at the options and see if there's any punny hints in them:
A) 8 - (5x + 2) = -5x - 6
B) 7z + 10 - z = 8z - 2(z - 5)
C) 8m - 4 = 5m + 8 - m
D) 6y + 5 = 6y - 5
Hmm, it seems like there's no obvious punchline here! Let's solve them instead:
A) 8 - (5x + 2) = -5x - 6:
Let's simplify:
8 - 5x - 2 = -5x - 6
6 - 5x = -5x - 6
12 = 0
Uh-oh! It seems like this equation doesn't make sense. No matter how hard we try, we can't make 12 equal to zero. So this equation has no solution!
B) 7z + 10 - z = 8z - 2(z - 5):
Let's simplify:
6z + 10 = 8z - 2z + 10
6z + 10 = 6z + 10
Hmm, it seems like the same expression on both sides. This means this equation is an identity!
So for the second question, the answer is B) 7z + 10 - z = 8z - 2(z - 5)!
I hope my humor-infused explanations helped you understand the solutions!
To solve the equation 3(x - 7) - x = 2x - 21, you need to simplify and isolate the variable x.
1. Distribute 3 to x and -7:
3x - 21 - x = 2x - 21
2. Combine like terms:
2x - 21 = 2x - 21
3. Subtract 2x from both sides:
-21 = -21
4. Since -21 is equal to -21, the equation is an identity, which means it holds true for all values of x. Therefore, the answer is C) Infinitely many solutions.
To determine which of the given equations is an identity:
A) 8-(5x+2) = -5x-6
B) 7z+10-z = 8z-2(z-5)
C) 8m-4 = 5m+8-m
D) 6y+5 = 6y-5
An identity is an equation that holds true for all values of the variable.
By simplifying each equation:
A) 8 - 5x - 2 = -5x - 6
6 - 5x = -5x - 6
Since -5x appears on both sides, it doesn't hold true for all values of x. Not an identity.
B) 7z + 10 - z = 8z - 2z + 10
6z + 10 = 6z + 10
Since the equation is unchanged on both sides, it holds true for all values of z. It is an identity.
C) 8m - 4 = 5m + 8 - m
7m - 4 = 8
Since there is a specific value of m (m = 2) that satisfies the equation, it is not an identity.
D) 6y + 5 = 6y - 5
10 = -5
The equation is contradictory and does not hold true for any value of y. Not an identity.
Therefore, the equation that is an identity is B) 7z+10-z=8z-2(z-5).