Solve 2-3(p-1)<7-(6p+5)+(1+p)

$$2 - 3 ( p - 1 ) < 7 - ( 6 p + 5 ) + ( 1 + p )$$

Solve for p

$$p<-1$$

Solution Steps

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

$$2-3p+3<7-\left(6p+5\right)+1+p$$

Add 2 and 3 to get 5.

$$5-3p<7-\left(6p+5\right)+1+p$$

To find the opposite of 6p+5, find the opposite of each term.

$$5-3p<7-6p-5+1+p$$

Subtract 5 from 7 to get 2.

$$5-3p<2-6p+1+p$$

Add 2 and 1 to get 3.

$$5-3p<3-6p+p$$

Combine -6p and p to get -5p.

$$5-3p<3-5p$$

Add 5p to both sides.

$$5-3p+5p<3$$

Combine -3p and 5p to get 2p.

$$5+2p<3$$

Subtract 5 from both sides.

$$2p<3-5$$

Subtract 5 from 3 to get -2.

$$2p<-2$$

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$p<\frac{-2}{2}$$

Divide -2 by 2 to get -1.

$$p<-1$$