Question

al details were added for this assignment.
determine if the following equation is an identity equation, a conditional equation, or an inconsistent equation.
$-9x - 4 + 6x = -6x + 5 - 7$
select the correct answer below:
○ identity equation
○ conditional equation
○ inconsistent equation

Explanation:

Step1: Simplify left side

Combine like terms: \(-9x + 6x - 4 = -3x - 4\)

Step2: Simplify right side

Combine like terms: \(-6x + (5 - 7) = -6x - 2\)

Step3: Rewrite equation

Now the equation is \(-3x - 4 = -6x - 2\)

Step4: Solve for x

Add \(6x\) to both sides: \(-3x + 6x - 4 = -2\) → \(3x - 4 = -2\)
Add 4 to both sides: \(3x = -2 + 4\) → \(3x = 2\)
Divide by 3: \(x = \frac{2}{3}\)
Since the equation is true only for \(x = \frac{2}{3}\) (not all real numbers, and not no solution), it's a conditional equation.

Answer:

B. Conditional equation