Solve 2x+1/3-x-1/2<0

$$\frac { 2 x + 1 } { 3 } - \frac { x - 1 } { 2 } < 0$$

Solve for x

$$x<-5$$

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.

$$2\left(2x+1\right)-3\left(x-1\right)<0$$

Use the distributive property to multiply 2 by 2x+1.

$$4x+2-3\left(x-1\right)<0$$

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

$$4x+2-3x+3<0$$

Combine 4x and -3x to get x.

$$x+2+3<0$$

Add 2 and 3 to get 5.

$$x+5<0$$

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$x<-5$$