Solve -2-3x/15<x+3/5

$$- \frac { 2 - 3 x } { 15 } < x + \frac { 3 } { 5 }$$

Solve for x

$$x>-\frac{11}{12}$$

Solution Steps

Multiply both sides of the equation by 15, the least common multiple of 15,5. Since 15 is positive, the inequality direction remains the same.

$$-\left(2-3x\right)<15x+9$$

To find the opposite of 2-3x, find the opposite of each term.

$$-2-\left(-3x\right)<15x+9$$

The opposite of -3x is 3x.

$$-2+3x<15x+9$$

Subtract 15x from both sides.

$$-2+3x-15x<9$$

Combine 3x and -15x to get -12x.

$$-2-12x<9$$

Add 2 to both sides.

$$-12x<9+2$$

Add 9 and 2 to get 11.

$$-12x<11$$

Divide both sides by -12. Since -12 is negative, the inequality direction is changed.

$$x>-\frac{11}{12}$$