Solve 1-2p-3/4<p/7+3/4

$$1- \frac{ 2p-3 }{ 4 } < \frac{ p }{ 7 } + \frac{ 3 }{ 4 }$$

Solve for p

$$p>\frac{14}{9}$$

Solution Steps

Multiply both sides of the equation by 28, the least common multiple of 4,7. Since 28 is positive, the inequality direction remains the same.

$$28-7\left(2p-3\right)<4p+21$$

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

$$28-14p+21<4p+21$$

Add 28 and 21 to get 49.

$$49-14p<4p+21$$

Subtract 4p from both sides.

$$49-14p-4p<21$$

Combine -14p and -4p to get -18p.

$$49-18p<21$$

Subtract 49 from both sides.

$$-18p<21-49$$

Subtract 49 from 21 to get -28.

$$-18p<-28$$

Divide both sides by -18. Since -18 is negative, the inequality direction is changed.

$$p>\frac{-28}{-18}$$

Reduce the fraction \frac{-28}{-18} to lowest terms by extracting and canceling out -2.

$$p>\frac{14}{9}$$