Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation. $\frac{x}{4}+\frac16=\frac{x}{3}$

• A. Identity 
• B. Conditional 
• C. Inconsistent 

Answer: (B)

Verified step by step guidance

1. Start by rewriting the given equation: \( \frac{x}{4} + \frac{1}{6} = \frac{x}{3} \).
2. To eliminate the fractions, find the least common denominator (LCD) of the fractions, which is 12.
3. Multiply every term in the equation by 12 to clear the fractions: \( 12 \times \frac{x}{4} + 12 \times \frac{1}{6} = 12 \times \frac{x}{3} \).
4. Simplify each term: \( 3x + 2 = 4x \).
5. Rearrange the equation to isolate \( x \) on one side: Subtract \( 3x \) from both sides to get \( 2 = x \). This shows the equation is conditional, as it holds true for a specific value of \( x \).