Solve 8x+7left(2-xright)<9-3left(x+1right)

$$8x+7 \left( 2-x \right) < 9-3 \left( x+1 \right)$$

Solve for x

$$x<-2$$

Solution Steps

Use the distributive property to multiply 7 by 2-x.

$$8x+14-7x<9-3\left(x+1\right)$$

Combine 8x and -7x to get x.

$$x+14<9-3\left(x+1\right)$$

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

$$x+14<9-3x-3$$

Subtract 3 from 9 to get 6.

$$x+14<6-3x$$

Add 3x to both sides.

$$x+14+3x<6$$

Combine x and 3x to get 4x.

$$4x+14<6$$

Subtract 14 from both sides.

$$4x<6-14$$

Subtract 14 from 6 to get -8.

$$4x<-8$$

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

$$x<\frac{-8}{4}$$

Divide -8 by 4 to get -2.

$$x<-2$$