Solving linear equations involving fractions means interpreting fractional numbers as constants or coefficients and using inverse operations, the distributive property, and equivalent transformations to isolate the variable while preserving equality. The learner can clear numerical denominators by multiplying every term by a common nonzero denominator, solve equations with fractions on one or both sides, and verify the solution by substitution; equations with variables in denominators or more advanced rational-equation cases are not included.
Fractions in an equation can make the steps look complicated. A helpful strategy is to clear the denominators by multiplying every term by the least common denominator.
Solve:
The denominators are and , so the least common denominator is .
Multiply every term on both sides by :
The denominators cancel:
Subtract from both sides:
Add to both sides:
Substitute into the original equation:
Both sides are equal, so the solution is
Remember: when clearing fractions, multiply every term by the common denominator so the equation remains equivalent.
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