1. Equations and Inequalities

Linear Equations

1. Equations and inequalities

Linear Equations

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Multiple Choice

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

Identity

Conditional

Inconsistent

Verified step by step guidance

Start by examining the given equation: $ \frac{x}{4} + \frac{1}{6} = \frac{x}{3} $. The goal is to solve for $ x $.

To eliminate the fractions, find the least common denominator (LCD) of the fractions involved. The denominators are 4, 6, and 3. The LCD is 12.

Multiply every term in the equation by the LCD (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 $: Subtract $ 3x $ from both sides to get $ 2 = x $. This is a conditional equation because it is true for a specific value of $ x $.