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

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

Solve for x

$$x<6$$

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.

$$3\left(x-\frac{1}{3}\right)-2\left(x-\frac{1}{2}\right)<6$$

Use the distributive property to multiply 3 by x-\frac{1}{3}.

$$3x+3\left(-\frac{1}{3}\right)-2\left(x-\frac{1}{2}\right)<6$$

Cancel out 3 and 3.

$$3x-1-2\left(x-\frac{1}{2}\right)<6$$

Use the distributive property to multiply -2 by x-\frac{1}{2}.

$$3x-1-2x-2\left(-\frac{1}{2}\right)<6$$

Multiply -2 times -\frac{1}{2}.

$$3x-1-2x+1<6$$

Combine 3x and -2x to get x.

$$x-1+1<6$$

Add -1 and 1 to get 0.

$$x<6$$