0. Review of College Algebra

Solving Linear Equations

0. Review of College Algebra

Solving 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 simplifying the given equation: $ \frac{x}{4} + \frac{1}{6} = \frac{x}{3} $. To eliminate the fractions, find a common denominator, which is 12.

Multiply each term by 12 to clear the fractions: $ 12 \times \frac{x}{4} + 12 \times \frac{1}{6} = 12 \times \frac{x}{3} $. This simplifies to $ 3x + 2 = 4x $.

Rearrange the equation to isolate terms involving x on one side: Subtract 3x from both sides to get $ 2 = x $.

Now that you have solved for x, check if the solution satisfies the original equation. Substitute x = 2 back into the original equation to verify.

Determine the type of equation: Since there is a specific solution (x = 2), the equation is conditional. An identity would be true for all values of x, and an inconsistent equation would have no solution.