Solve 4x+4-(x+1)<5(x-1)

$$4 x + 4 - ( x + 1 ) < 5 ( x - 1 )$$

Solve for x

$$x>4$$

Solution Steps

To find the opposite of x+1, find the opposite of each term.

$$4x+4-x-1<5\left(x-1\right)$$

Combine 4x and -x to get 3x.

$$3x+4-1<5\left(x-1\right)$$

Subtract 1 from 4 to get 3.

$$3x+3<5\left(x-1\right)$$

Use the distributive property to multiply 5 by x-1.

$$3x+3<5x-5$$

Subtract 5x from both sides.

$$3x+3-5x<-5$$

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

$$-2x+3<-5$$

Subtract 3 from both sides.

$$-2x<-5-3$$

Subtract 3 from -5 to get -8.

$$-2x<-8$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$x>\frac{-8}{-2}$$

Divide -8 by -2 to get 4.

$$x>4$$