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

$$\frac { 3 ( 2 x + 7 ) } { - 3 } > x + 1$$

Solve for x

$$x<-\frac{8}{3}$$

Solution Steps

Multiply both sides of the equation by -3. Since -3 is negative, the inequality direction is changed.

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

Use the distributive property to multiply 3 by 2x+7.

$$6x+21<-3x-3$$

Add 3x to both sides.

$$6x+21+3x<-3$$

Combine 6x and 3x to get 9x.

$$9x+21<-3$$

Subtract 21 from both sides.

$$9x<-3-21$$

Subtract 21 from -3 to get -24.

$$9x<-24$$

Divide both sides by 9. Since 9 is positive, the inequality direction remains the same.

$$x<\frac{-24}{9}$$

Reduce the fraction \frac{-24}{9} to lowest terms by extracting and canceling out 3.

$$x<-\frac{8}{3}$$