Example

Solving 15(n+3)=14(n+2)\frac{1}{5}(n + 3) = \frac{1}{4}(n + 2) by Clearing Fractions

To solve the linear equation 15(n+3)=14(n+2)\frac{1}{5}(n + 3) = \frac{1}{4}(n + 2), clear the fractions first by multiplying both sides by the least common denominator (LCD) of 15\frac{1}{5} and 14\frac{1}{4}, which is 2020. Multiplying both sides by 2020 gives 2015(n+3)=2014(n+2)20 \cdot \frac{1}{5}(n + 3) = 20 \cdot \frac{1}{4}(n + 2), which simplifies to 4(n+3)=5(n+2)4(n + 3) = 5(n + 2). Distribute the constants to obtain 4n+12=5n+104n + 12 = 5n + 10. Collect the variable terms on one side (for example, by subtracting 4n4n from both sides to get 12=n+1012 = n + 10) and the constant terms on the other (subtracting 1010 gives 2=n2 = n). The solution is n=2n = 2.

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Updated 2026-05-02

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