Solve 2(1-2x)-x>3(x+1)+7

$$2 ( 1 - 2 x ) - x > 3 ( x + 1 ) + 7$$

Solve for x

$$x<-1$$

Solution Steps

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

$$2-4x-x>3\left(x+1\right)+7$$

Combine -4x and -x to get -5x.

$$2-5x>3\left(x+1\right)+7$$

Use the distributive property to multiply 3 by x+1.

$$2-5x>3x+3+7$$

Add 3 and 7 to get 10.

$$2-5x>3x+10$$

Subtract 3x from both sides.

$$2-5x-3x>10$$

Combine -5x and -3x to get -8x.

$$2-8x>10$$

Subtract 2 from both sides.

$$-8x>10-2$$

Subtract 2 from 10 to get 8.

$$-8x>8$$

Divide both sides by -8. Since -8 is negative, the inequality direction is changed.

$$x<\frac{8}{-8}$$

Divide 8 by -8 to get -1.

$$x<-1$$