Solve -3(2x-1)<-2[4+4(x+2)]

$$- 3 ( 2 x - 1 ) < - 2 [ 4 + 4 ( x + 2 ) ]$$

Solve for x

$$x<-\frac{27}{2}$$

Solution Steps

Use the distributive property to multiply -3 by 2x-1.

$$-6x+3<-2\left(4+4\left(x+2\right)\right)$$

Use the distributive property to multiply 4 by x+2.

$$-6x+3<-2\left(4+4x+8\right)$$

Add 4 and 8 to get 12.

$$-6x+3<-2\left(12+4x\right)$$

Use the distributive property to multiply -2 by 12+4x.

$$-6x+3<-24-8x$$

Add 8x to both sides.

$$-6x+3+8x<-24$$

Combine -6x and 8x to get 2x.

$$2x+3<-24$$

Subtract 3 from both sides.

$$2x<-24-3$$

Subtract 3 from -24 to get -27.

$$2x<-27$$

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

$$x<-\frac{27}{2}$$