Solve x/2-1/3>2x/3+1

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

Solve for x

$$x<-8$$

Solution Steps

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

$$3x-2>2\times 2x+6$$

Multiply 2 and 2 to get 4.

$$3x-2>4x+6$$

Subtract 4x from both sides.

$$3x-2-4x>6$$

Combine 3x and -4x to get -x.

$$-x-2>6$$

Add 2 to both sides.

$$-x>6+2$$

Add 6 and 2 to get 8.

$$-x>8$$

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

$$x<-8$$