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

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

Solve for x

$$x>-\frac{8}{7}$$

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.

$$2\times 2\left(1-x\right)<3x+12$$

Multiply 2 and 2 to get 4.

$$4\left(1-x\right)<3x+12$$

Use the distributive property to multiply 4 by 1-x.

$$4-4x<3x+12$$

Subtract 3x from both sides.

$$4-4x-3x<12$$

Combine -4x and -3x to get -7x.

$$4-7x<12$$

Subtract 4 from both sides.

$$-7x<12-4$$

Subtract 4 from 12 to get 8.

$$-7x<8$$

Divide both sides by -7. Since -7 is negative, the inequality direction is changed.

$$x>-\frac{8}{7}$$