Solve 5+x/3-x+6/2<-1

$$\frac { 5 + x } { 3 } - \frac { x + 6 } { 2 } < - 1$$

Solve for x

$$x>-2$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

$$2\left(5+x\right)-3\left(x+6\right)<-6$$

Use the distributive property to multiply 2 by 5+x.

$$10+2x-3\left(x+6\right)<-6$$

Use the distributive property to multiply -3 by x+6.

$$10+2x-3x-18<-6$$

Combine 2x and -3x to get -x.

$$10-x-18<-6$$

Subtract 18 from 10 to get -8.

$$-8-x<-6$$

Add 8 to both sides.

$$-x<-6+8$$

Add -6 and 8 to get 2.

$$-x<2$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x>-2$$