Question

Classify the equation as a conditional equation, an identity, or a contradiction.

11(8c + 5) - 8c = 2(40c + 25) + 5

Select the correct answer below:
Conditional equation
Identity
Contradiction

Answer 1

11(8c + 5) - 8c = 2(40c + 25) + 5

88c + 55 - 8c = 80c + 50 + 5

80c + 55 = 80c + 55

This equation is an identity.

Answer 2

After simplifying the equation 11(8c + 5) - 8c = 2(40c + 25) + 5, it becomes clear that it is an identity, as both sides reduce to the same expression, 80c + 55, and is true for all values of c.

Step-by-step explanation:

To classify the equation 11(8c + 5) - 8c = 2(40c + 25) + 5 as a conditional equation, an identity, or a contradiction, we need to simplify both sides of the equation. First, distribute the 11 and 2 across the parentheses:

88c + 55 - 8c = 80c + 50 + 5

Now, combine like terms:

80c + 55 = 80c + 55

As we can see, the equation simplifies to an identity, because after simplification, both sides of the equation are the same. An identity is an equation that is true for all values of the variable.