Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation. $\frac{x}{4}\)+$\frac$16=\(\frac{x}{3}$

Identity

Conditional

Inconsistent

Verified step by step guidance

Start by rewriting the given equation: $ \frac{x}{4} + \frac{1}{6} = \frac{x}{3} $.

To eliminate the fractions, find the least common denominator (LCD) of the fractions, which is 12.

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} $.

Simplify each term: $ 3x + 2 = 4x $.

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 $.

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Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation. $\frac{x}{4}\)+\(\frac\)16=\(\frac{x}{3}$