Solve 1/2t-3/4<-2/5t+3/5

$$\frac { 1 } { 2 } t - \frac { 3 } { 4 } < - \frac { 2 } { 5 } t + \frac { 3 } { 5 }$$

Solve for t

$$t<\frac{3}{2}$$

Solution Steps

Add \frac{2}{5}t to both sides.

$$\frac{1}{2}t-\frac{3}{4}+\frac{2}{5}t<\frac{3}{5}$$

Combine \frac{1}{2}t and \frac{2}{5}t to get \frac{9}{10}t.

$$\frac{9}{10}t-\frac{3}{4}<\frac{3}{5}$$

Add \frac{3}{4} to both sides.

$$\frac{9}{10}t<\frac{3}{5}+\frac{3}{4}$$

Least common multiple of 5 and 4 is 20. Convert \frac{3}{5} and \frac{3}{4} to fractions with denominator 20.

$$\frac{9}{10}t<\frac{12}{20}+\frac{15}{20}$$

Since \frac{12}{20} and \frac{15}{20} have the same denominator, add them by adding their numerators.

$$\frac{9}{10}t<\frac{12+15}{20}$$

Add 12 and 15 to get 27.

$$\frac{9}{10}t<\frac{27}{20}$$

Multiply both sides by \frac{10}{9}, the reciprocal of \frac{9}{10}. Since \frac{9}{10} is positive, the inequality direction remains the same.

$$t<\frac{27}{20}\times \frac{10}{9}$$

Multiply \frac{27}{20} times \frac{10}{9} by multiplying numerator times numerator and denominator times denominator.

$$t<\frac{27\times 10}{20\times 9}$$

Do the multiplications in the fraction \frac{27\times 10}{20\times 9}.

$$t<\frac{270}{180}$$

Reduce the fraction \frac{270}{180} to lowest terms by extracting and canceling out 90.

$$t<\frac{3}{2}$$