Solve x-11/4<-x+22/7

$$\frac { x - 11 } { 4 } < - \frac { x + 22 } { 7 }$$

Solve for x

$$x<-1$$

Solution Steps

Multiply both sides of the equation by 28, the least common multiple of 4,7. Since 28 is positive, the inequality direction remains the same.

$$7\left(x-11\right)<-4\left(x+22\right)$$

Use the distributive property to multiply 7 by x-11.

$$7x-77<-4\left(x+22\right)$$

Use the distributive property to multiply -4 by x+22.

$$7x-77<-4x-88$$

Add 4x to both sides.

$$7x-77+4x<-88$$

Combine 7x and 4x to get 11x.

$$11x-77<-88$$

Add 77 to both sides.

$$11x<-88+77$$

Add -88 and 77 to get -11.

$$11x<-11$$

Divide both sides by 11. Since 11 is positive, the inequality direction remains the same.

$$x<\frac{-11}{11}$$

Divide -11 by 11 to get -1.

$$x<-1$$