Solve x-x+2/12<5x/2

$$x - \frac { x + 2 } { 12 } < \frac { 5 x } { 2 }$$

Solve for x

$$x>-\frac{2}{19}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 12,2. Since 12 is positive, the inequality direction remains the same.

$$12x-\left(x+2\right)<6\times 5x$$

To find the opposite of x+2, find the opposite of each term.

$$12x-x-2<6\times 5x$$

Combine 12x and -x to get 11x.

$$11x-2<6\times 5x$$

Multiply 6 and 5 to get 30.

$$11x-2<30x$$

Subtract 30x from both sides.

$$11x-2-30x<0$$

Combine 11x and -30x to get -19x.

$$-19x-2<0$$

Add 2 to both sides. Anything plus zero gives itself.

$$-19x<2$$

Divide both sides by -19. Since -19 is negative, the inequality direction is changed.

$$x>-\frac{2}{19}$$