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\frac{5}{4}x+1<6
Swap sides so that all variable terms are on the left hand side. This changes the sign direction.
\frac{5}{4}x<6-1
Subtract 1 from both sides.
\frac{5}{4}x<5
Subtract 1 from 6 to get 5.
x<5\times \frac{4}{5}
Multiply both sides by \frac{4}{5}, the reciprocal of \frac{5}{4}. Since \frac{5}{4} is positive, the inequality direction remains the same.
x<4
Cancel out 5 and 5.