Solve x-1/2-x+1/3<4x+1/6

$$\frac { x - 1 } { 2 } - \frac { x + 1 } { 3 } < \frac { 4 x + 1 } { 6 }$$

Solve for x

$$x>-2$$

Solution Steps

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

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

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

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

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

$$3x-3-2x-2<4x+1$$

Combine 3x and -2x to get x.

$$x-3-2<4x+1$$

Subtract 2 from -3 to get -5.

$$x-5<4x+1$$

Subtract 4x from both sides.

$$x-5-4x<1$$

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

$$-3x-5<1$$

Add 5 to both sides.

$$-3x<1+5$$

Add 1 and 5 to get 6.

$$-3x<6$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$x>\frac{6}{-3}$$

Divide 6 by -3 to get -2.

$$x>-2$$