Solve 8(x+1)+1^2<3(2x)-1

$$8 ( x + 1 ) + 1 ^ { 2 } < 3 ( 2 x ) - 1$$

Solve for x

$$x<-5$$

Solution Steps

Use the distributive property to multiply 8 by x+1.

$$8x+8+1^{2}<3\times 2x-1$$

Calculate 1 to the power of 2 and get 1.

$$8x+8+1<3\times 2x-1$$

Add 8 and 1 to get 9.

$$8x+9<3\times 2x-1$$

Multiply 3 and 2 to get 6.

$$8x+9<6x-1$$

Subtract 6x from both sides.

$$8x+9-6x<-1$$

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

$$2x+9<-1$$

Subtract 9 from both sides.

$$2x<-1-9$$

Subtract 9 from -1 to get -10.

$$2x<-10$$

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

$$x<\frac{-10}{2}$$

Divide -10 by 2 to get -5.

$$x<-5$$