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

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

Solve for x

$$x>-3$$

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.

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

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

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

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

$$-x+3<6$$

Subtract 3 from both sides.

$$-x<6-3$$

Subtract 3 from 6 to get 3.

$$-x<3$$

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

$$x>-3$$