Example

Solving 12(m3)=14(m7)\frac{1}{2}(m - 3) = \frac{1}{4}(m - 7) by Clearing Fractions

To solve the linear equation 12(m3)=14(m7)\frac{1}{2}(m - 3) = \frac{1}{4}(m - 7), find the least common denominator (LCD) of 12\frac{1}{2} and 14\frac{1}{4}, which is 44. Multiply both sides by the LCD to clear the fractions: 412(m3)=414(m7)4 \cdot \frac{1}{2}(m - 3) = 4 \cdot \frac{1}{4}(m - 7). This simplifies to 2(m3)=1(m7)2(m - 3) = 1(m - 7). Distribute the constants to get 2m6=m72m - 6 = m - 7. Subtract mm from both sides to collect the variable terms, yielding m6=7m - 6 = -7. Add 66 to both sides to isolate mm, resulting in the final solution m=1m = -1.

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Updated 2026-05-02

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