Which equation 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
I'm on this two ):
To determine which equation is an identity, we need to find an equation that is true for all values of the variable(s) involved. Let's analyze each option:
a. 7 - (9x + 3) = -9x - 4
To simplify, let's distribute the negative sign inside the parentheses:
7 - 9x - 3 = -9x - 4
Combine like terms:
4 - 9x = -9x - 4
Add 9x to both sides:
4 = -4
Since this equation is contradictory (4 cannot be equal to -4), option a is not an identity.
b. 6m - 5 = 7m + 5 - m
Combine the like terms:
6m - 5 = 6m + 5
Subtract 6m from both sides:
-5 = 5
Like option a, this equation is also contradictory, as -5 cannot be equal to 5. So, option b is not an identity.
c. 10p + 6 - p = 12p - 3(p - 2)
Let's simplify the equation step by step:
10p + 6 - p = 12p - 3p + 6
Combine the like terms:
9p + 6 = 9p + 6
Subtract 9p and 6 from both sides:
0 = 0
In this case, the equation simplifies to 0 = 0, which is true for any value of p. Therefore, option c is the identity equation.
d. 3y + 2 = 3y - 2
Subtract 3y from both sides:
2 = -2
Similar to options a and b, the equation in option d is also contradictory. 2 cannot be equal to -2. Hence, option d is not an identity.
Therefore, the equation that is an identity is option c: 10p + 6 - p = 12p - 3(p - 2).
To determine which equation is an identity, we need to check if the equation is true for all possible values of the variable(s). Let's examine each equation:
a. 7-(9x+3) = -9x-4
To solve this equation, we can start by simplifying both sides:
7 - 9x - 3 = -9x - 4
4 - 9x = -9x - 4
Notice that the variable term (-9x) appears on both sides. If we perform any operations to eliminate it, both sides will become equal to the constant term (-4). This means that this equation is an identity since it holds true for any value of x.
b. 6m - 5 = 7m + 5 - m
Let's simplify the equation:
6m - 5 = 7m - m + 5
Combining like terms, we get:
6m - 5 = 6m + 5
Here, we have different constant terms on both sides of the equation (-5 and +5), so no matter what value we plug in for m, the equation will not hold true. Therefore, this equation is not an identity.
c. 10p + 6 - p = 12p - 3(p - 2)
Simplifying the equation:
9p + 6 = 12p - 3p + 6
Combining like terms:
9p + 6 = 9p + 6
The variable term (9p) appears on both sides, and the constant terms are the same (6 and 6), meaning the equation holds true regardless of the value of p. Therefore, this equation is an identity.
d. 3y + 2 = 3y - 2
We can simplify this equation:
3y + 2 = 3y - 2
Rearranging the equation to have the variable terms on one side:
(3y - 3y) + 2 = -2
Simplifying further:
0 + 2 = -2
Now, we have different constant terms on both sides (2 and -2), which means the equation is not true for any value of y. Consequently, this equation is not an identity.
In conclusion, the equation that is an identity is option (a): 7 - (9x + 3) = -9x - 4.