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

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

Solve for x

$$x>5$$

Solution Steps

Multiply both sides of the equation by 15, the least common multiple of 3,5. Since 15 is positive, the inequality direction remains the same.

$$5\left(x-2\right)-3\left(5-2x\right)<15x-45$$

Use the distributive property to multiply 5 by x-2.

$$5x-10-3\left(5-2x\right)<15x-45$$

Use the distributive property to multiply -3 by 5-2x.

$$5x-10-15+6x<15x-45$$

Subtract 15 from -10 to get -25.

$$5x-25+6x<15x-45$$

Combine 5x and 6x to get 11x.

$$11x-25<15x-45$$

Subtract 15x from both sides.

$$11x-25-15x<-45$$

Combine 11x and -15x to get -4x.

$$-4x-25<-45$$

Add 25 to both sides.

$$-4x<-45+25$$

Add -45 and 25 to get -20.

$$-4x<-20$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x>\frac{-20}{-4}$$

Divide -20 by -4 to get 5.

$$x>5$$