Solve 4p-3(6-15p)>4p-3/-2

$$4 p - 3 ( 6 - 15 p ) > \frac { 4 p - 3 } { - 2 }$$

Solve for p

$$p>\frac{13}{34}$$

Solution Steps

Multiply both sides of the equation by -2. Since -2 is negative, the inequality direction is changed.

$$-8p+6\left(6-15p\right)<4p-3$$

Use the distributive property to multiply 6 by 6-15p.

$$-8p+36-90p<4p-3$$

Combine -8p and -90p to get -98p.

$$-98p+36<4p-3$$

Subtract 4p from both sides.

$$-98p+36-4p<-3$$

Combine -98p and -4p to get -102p.

$$-102p+36<-3$$

Subtract 36 from both sides.

$$-102p<-3-36$$

Subtract 36 from -3 to get -39.

$$-102p<-39$$

Divide both sides by -102. Since -102 is negative, the inequality direction is changed.

$$p>\frac{-39}{-102}$$

Reduce the fraction \frac{-39}{-102} to lowest terms by extracting and canceling out -3.

$$p>\frac{13}{34}$$