Solve 2(x-1)+25-8-(x+5)<(3x-4)-x-(8-x)

$$2(x-1)+25-8-(x+5) < (3x-4)-x-(8-x)$$

Solve for x

$$x>11$$

Solution Steps

Use the distributive property to multiply 2 by x-1.

$$2x-2+25-8-\left(x+5\right)<3x-4-x-\left(8-x\right)$$

Add -2 and 25 to get 23.

$$2x+23-8-\left(x+5\right)<3x-4-x-\left(8-x\right)$$

Subtract 8 from 23 to get 15.

$$2x+15-\left(x+5\right)<3x-4-x-\left(8-x\right)$$

To find the opposite of x+5, find the opposite of each term.

$$2x+15-x-5<3x-4-x-\left(8-x\right)$$

Combine 2x and -x to get x.

$$x+15-5<3x-4-x-\left(8-x\right)$$

Subtract 5 from 15 to get 10.

$$x+10<3x-4-x-\left(8-x\right)$$

Combine 3x and -x to get 2x.

$$x+10<2x-4-\left(8-x\right)$$

To find the opposite of 8-x, find the opposite of each term.

$$x+10<2x-4-8-\left(-x\right)$$

The opposite of -x is x.

$$x+10<2x-4-8+x$$

Subtract 8 from -4 to get -12.

$$x+10<2x-12+x$$

Combine 2x and x to get 3x.

$$x+10<3x-12$$

Subtract 3x from both sides.

$$x+10-3x<-12$$

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

$$-2x+10<-12$$

Subtract 10 from both sides.

$$-2x<-12-10$$

Subtract 10 from -12 to get -22.

$$-2x<-22$$

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

$$x>\frac{-22}{-2}$$

Divide -22 by -2 to get 11.

$$x>11$$