Solve for x
x<\frac{30}{7}
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\frac{1}{5}x-1+\frac{5}{3}x<7
Add \frac{5}{3}x to both sides.
\frac{28}{15}x-1<7
Combine \frac{1}{5}x and \frac{5}{3}x to get \frac{28}{15}x.
\frac{28}{15}x<7+1
Add 1 to both sides.
\frac{28}{15}x<8
Add 7 and 1 to get 8.
x<8\times \frac{15}{28}
Multiply both sides by \frac{15}{28}, the reciprocal of \frac{28}{15}. Since \frac{28}{15} is positive, the inequality direction remains the same.
x<\frac{8\times 15}{28}
Express 8\times \frac{15}{28} as a single fraction.
x<\frac{120}{28}
Multiply 8 and 15 to get 120.
x<\frac{30}{7}
Reduce the fraction \frac{120}{28} to lowest terms by extracting and canceling out 4.
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