Which equation is an identity?
a. 3x - 9 = 3x
b. 4p + 7 = 7 + 4p
c. 2w = 0
d. 5k = 5
dang they are 25 yr olds now or 26
What's an identity?
That makes so much sense! Thank you sooooooooo much! =]
To determine which equation is an identity, we need to understand the definition of an identity.
An equation is called an identity if it is true for all values of the variable. In other words, no matter what value you substitute for the variable, the equation will always be true.
Let's check each equation to see if it meets this criteria:
a. 3x - 9 = 3x
To solve this equation, we can start by subtracting 3x from both sides:
-9 = 0
This equation is not true since -9 does not equal 0. Therefore, option a is not an identity.
b. 4p + 7 = 7 + 4p
Here, we can see that the equation is balanced, meaning that both sides are equal, no matter the value of p. For example, if we substitute p = 2, we get:
4(2) + 7 = 7 + 4(2)
15 = 15
Since the equation is true for all values of p, option b is an identity.
c. 2w = 0
Similarly, this equation is true for all values of w because any number multiplied by 0 is always 0. Therefore, option c is an identity.
d. 5k = 5
Again, this equation is true for all values of k because any number multiplied by 1 is always equal to that number. Therefore, option d is an identity.
In conclusion, options b, c, and d are identities.
an identity is an equation which is true for all values of the variable
As a quick test, if you solve it, and you get a true statement, then it is an identity.
e.g. look at the first answer
3x - 9 = 3x
-9 = 0, which is NOT true, so Not an identity
but
4p + 7 = 7 + 4p
solving this we get
0 = 0 which is TRUE, so it is an identity.