Solve for a
a<\frac{4}{7}
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\frac{1}{4}a+2a+3a<3
Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.
\frac{9}{4}a+3a<3
Combine \frac{1}{4}a and 2a to get \frac{9}{4}a.
\frac{21}{4}a<3
Combine \frac{9}{4}a and 3a to get \frac{21}{4}a.
a<3\times \frac{4}{21}
Multiply both sides by \frac{4}{21}, the reciprocal of \frac{21}{4}. Since \frac{21}{4} is positive, the inequality direction remains the same.
a<\frac{3\times 4}{21}
Express 3\times \frac{4}{21} as a single fraction.
a<\frac{12}{21}
Multiply 3 and 4 to get 12.
a<\frac{4}{7}
Reduce the fraction \frac{12}{21} to lowest terms by extracting and canceling out 3.
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