Solve 1/3+-1/2(5-t)<0

$$\frac { 1 } { 3 } + - \frac { 1 } { 2 } ( 5 - t ) < 0$$

Solve for t

$$t<\frac{13}{3}$$

Solution Steps

Use the distributive property to multiply -\frac{1}{2} by 5-t.

$$\frac{1}{3}-\frac{1}{2}\times 5-\frac{1}{2}\left(-1\right)t<0$$

Express -\frac{1}{2}\times 5 as a single fraction.

$$\frac{1}{3}+\frac{-5}{2}-\frac{1}{2}\left(-1\right)t<0$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$\frac{1}{3}-\frac{5}{2}-\frac{1}{2}\left(-1\right)t<0$$

Multiply -\frac{1}{2} and -1 to get \frac{1}{2}.

$$\frac{1}{3}-\frac{5}{2}+\frac{1}{2}t<0$$

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{5}{2} to fractions with denominator 6.

$$\frac{2}{6}-\frac{15}{6}+\frac{1}{2}t<0$$

Since \frac{2}{6} and \frac{15}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-15}{6}+\frac{1}{2}t<0$$

Subtract 15 from 2 to get -13.

$$-\frac{13}{6}+\frac{1}{2}t<0$$

Add \frac{13}{6} to both sides. Anything plus zero gives itself.

$$\frac{1}{2}t<\frac{13}{6}$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}. Since \frac{1}{2} is positive, the inequality direction remains the same.

$$t<\frac{13}{6}\times 2$$

Express \frac{13}{6}\times 2 as a single fraction.

$$t<\frac{13\times 2}{6}$$

Multiply 13 and 2 to get 26.

$$t<\frac{26}{6}$$

Reduce the fraction \frac{26}{6} to lowest terms by extracting and canceling out 2.

$$t<\frac{13}{3}$$