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

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

Solve for x

$$x>-22$$

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.

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

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

$$2x-4-3\left(x+2\right)<6\times 2$$

Use the distributive property to multiply -3 by x+2.

$$2x-4-3x-6<6\times 2$$

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

$$-x-4-6<6\times 2$$

Subtract 6 from -4 to get -10.

$$-x-10<6\times 2$$

Multiply 6 and 2 to get 12.

$$-x-10<12$$

Add 10 to both sides.

$$-x<12+10$$

Add 12 and 10 to get 22.

$$-x<22$$

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

$$x>-22$$