Question

Classify the equation −6x−5=9x=3x−5×3 as a conditional equation, an identity, or a contradiction.

a) Conditional equation
b) Identity
c) Contradiction

Answer 1

The given equation −6x−5=9x=3x−5×3 can be classified as a contradiction.

Step-by-step explanation:

This equation can be classified as a contradiction. To determine this, we need to simplify the equation and see if it leads to a contradiction. By combining like terms and simplifying both sides, we get:

-6x - 5 = 9x - 2x - 5 * 3

-6x - 5 = 7x - 15

Combining like terms again, we get:

-6x = 7x - 10

Bringing all the x-terms to one side, we have:

-6x - 7x = -10

-13x = -10

Finally, solving for x, we get:

x = \frac{-10}{-13}

x = \frac{10}{13}

This solution is a real number, so it is not a contradiction. Therefore, the given equation is a contradiction.