1Cademy - Solving $$\frac{1}{12}x + \frac{5}{6} = \frac{3}{4}$$ by Clearing Fractions

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Strategy for Solving Equations with Fraction or Decimal Coefficients

Example

Solving $\frac{1}{12}x + \frac{5}{6} = \frac{3}{4}$ by Clearing Fractions

To solve the linear equation $\frac{1}{12}x + \frac{5}{6} = \frac{3}{4}$ by clearing fractions, apply the strategy for solving equations with fraction or decimal coefficients.

Step 1: Find the least common denominator (LCD) of all the fractions in the equation. The denominators are $12$ , $6$ , and $4$ . The LCD is $12$ .

Step 2: Multiply both sides of the equation by the LCD, $12$ , to clear the fractions: $12\left(\frac{1}{12}x + \frac{5}{6}\right) = 12\left(\frac{3}{4}\right)$

Use the Distributive Property on the left side: $12\left(\frac{1}{12}x\right) + 12\left(\frac{5}{6}\right) = 12\left(\frac{3}{4}\right)$

Simplify each term to eliminate the fractions: $x + 10 = 9$

Step 3: Solve using the general strategy for solving linear equations. Subtract $10$ from both sides to isolate the variable term: $x + 10 - 10 = 9 - 10$ $x = -1$

Finally, check the solution by substituting $-1$ for $x$ in the original equation: $\frac{1}{12}(-1) + \frac{5}{6} \stackrel{?}{=} \frac{3}{4}$ $-\frac{1}{12} + \frac{10}{12} \stackrel{?}{=} \frac{9}{12}$ $\frac{9}{12} = \frac{9}{12} \checkmark$ Because both sides are equal, $x = -1$ is confirmed as the correct solution.

Updated 2026-05-25

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OpenStax Intermediate Algebra

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