Solve 4(x+2)<-8-2(2x+1)

$$4 ( x + 2 ) < - 8 - 2 ( 2 x + 1 )$$

Solve for x

$$x<-\frac{9}{4}$$

Solution Steps

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

$$4x+8<-8-2\left(2x+1\right)$$

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

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

Subtract 2 from -8 to get -10.

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

Add 4x to both sides.

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

Combine 4x and 4x to get 8x.

$$8x+8<-10$$

Subtract 8 from both sides.

$$8x<-10-8$$

Subtract 8 from -10 to get -18.

$$8x<-18$$

Divide both sides by 8. Since 8 is positive, the inequality direction remains the same.

$$x<\frac{-18}{8}$$

Reduce the fraction \frac{-18}{8} to lowest terms by extracting and canceling out 2.

$$x<-\frac{9}{4}$$