Questions: Determine if the following equation is an identity equation, a conditional equation, or an inconsistent equation -6x + 6x - 6 = 2 - 5

Solution Steps

To determine the type of equation, we need to simplify the given equation and see if it holds true for all values of \( x \), for some values of \( x \), or for no values of \( x \).

1. Simplify the left-hand side of the equation.
2. Compare the simplified left-hand side with the right-hand side.
3. Determine if the equation is always true (identity), true for some values (conditional), or never true (inconsistent).

First, we simplify the given equation: \[ -6x + 6x - 6 = 2 - 5 \]

Combine like terms on the left-hand side: \[ (-6x + 6x) - 6 = 2 - 5 \]

Since \(-6x + 6x = 0\), the equation simplifies to: \[ 0 - 6 = 2 - 5 \]

Next, simplify both sides of the equation: \[ -6 = 2 - 5 \]

Calculate the right-hand side: \[ 2 - 5 = -3 \]

So the equation becomes: \[ -6 = -3 \]

Since \(-6\) is not equal to \(-3\), the equation is false. Therefore, the given equation is an inconsistent equation.

Final Answer