I'm suppose to 'determine whether the equation is an identity or a conditional equation.

A) -6(x-3)+5 = -2x+10
I solved this and got x = 13/4. How am I suppose to figure out whether its identity or conditional equation?

Same goes with this problem
B) -7(x-3)+4x = 3(7-x)
-7x+21+4x = 21-3x
-21-3x = 21- 3x ?

(A)

x=13/4 means that the equation is valid only at x=13/4, and is not valid elsewhere.
Would that be an identity or a conditional equation?

(B)
There was an arithmetical error on the last line:
-7x+21+4x = 21-3x
+21-3x = 21- 3x
So after cancelling, we get
21=21
Would that be a conditional equation or an identity (i.e. true for all values of x)?

Determine whether the given equation is identity, a false equation, or a open sentence.

a + 5 = a

To determine whether an equation is an identity or a conditional equation, you need to verify if the equation holds true for all possible values of the variable.

For problem A, you solved it and obtained x = 13/4. Now, to check if it is an identity or a conditional equation, you substitute the value of x back into the original equation.

-6(x-3) + 5 = -2x + 10

Substituting x = 13/4:

-6(13/4 - 3) + 5 = -2(13/4) +10

Simplifying:

-6(-7/4) + 5 = -26/4 + 10
42/4 + 5 = -26/4 + 40/4
42/4 + 5 = 14/4 + 40/4
47/4 = 54/4

Since 47/4 is not equal to 54/4, the equation does not hold true for all values of x. Therefore, this equation is a conditional equation.

For problem B, you've simplified it to:

-21 - 3x = 21 - 3x

As you can see, the expression on both sides of the equation is identical. So, no matter what value you substitute in for x, the equation will always be true. This indicates that the equation is an identity.

In summary:
- For problem A, the equation is a conditional equation since it does not hold true for all values of x.
- For problem B, the equation is an identity since it holds true for all values of x.