Example

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

To solve the linear equation 12(m−3)=14(m−7)\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: 4⋅12(m−3)=4⋅14(m−7)4 \cdot \frac{1}{2}(m - 3) = 4 \cdot \frac{1}{4}(m - 7). This simplifies to 2(m−3)=1(m−7)2(m - 3) = 1(m - 7). Distribute the constants to get 2m−6=m−72m - 6 = m - 7. Subtract mm from both sides to collect the variable terms, yielding m−6=−7m - 6 = -7. Add 66 to both sides to isolate mm, resulting in the final solution m=−1m = -1.

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Updated 2026-06-03

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