Solve 1-t/2<3t-7/3

$$\frac { 1 - t } { 2 } < \frac { 3 t - 7 } { 3 }$$

Solve for t

$$t>\frac{17}{9}$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 2,3. Since 6 is positive, the inequality direction remains the same.

$$3\left(1-t\right)<2\left(3t-7\right)$$

Use the distributive property to multiply 3 by 1-t.

$$3-3t<2\left(3t-7\right)$$

Use the distributive property to multiply 2 by 3t-7.

$$3-3t<6t-14$$

Subtract 6t from both sides.

$$3-3t-6t<-14$$

Combine -3t and -6t to get -9t.

$$3-9t<-14$$

Subtract 3 from both sides.

$$-9t<-14-3$$

Subtract 3 from -14 to get -17.

$$-9t<-17$$

Divide both sides by -9. Since -9 is negative, the inequality direction is changed.

$$t>\frac{-17}{-9}$$

Fraction \frac{-17}{-9} can be simplified to \frac{17}{9} by removing the negative sign from both the numerator and the denominator.

$$t>\frac{17}{9}$$