Solve 2x+2/5-x-1/2<2

$$\frac { 2 x + 2 } { 5 } - \frac { x - 1 } { 2 } < 2$$

Solve for x

$$x>-11$$

Solution Steps

Multiply both sides of the equation by 10, the least common multiple of 5,2. Since 10 is positive, the inequality direction remains the same.

$$2\left(2x+2\right)-5\left(x-1\right)<20$$

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

$$4x+4-5\left(x-1\right)<20$$

Use the distributive property to multiply -5 by x-1.

$$4x+4-5x+5<20$$

Combine 4x and -5x to get -x.

$$-x+4+5<20$$

Add 4 and 5 to get 9.

$$-x+9<20$$

Subtract 9 from both sides.

$$-x<20-9$$

Subtract 9 from 20 to get 11.

$$-x<11$$

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

$$x>-11$$