Solve 5/9x+2<3/5x-3

$$\frac { 5 } { 9 } x + 2 < \frac { 3 } { 5 } x - 3$$

Solve for x

$$x>\frac{225}{2}$$

Solution Steps

Subtract \frac{3}{5}x from both sides.

$$\frac{5}{9}x+2-\frac{3}{5}x<-3$$

Combine \frac{5}{9}x and -\frac{3}{5}x to get -\frac{2}{45}x.

$$-\frac{2}{45}x+2<-3$$

Subtract 2 from both sides.

$$-\frac{2}{45}x<-3-2$$

Subtract 2 from -3 to get -5.

$$-\frac{2}{45}x<-5$$

Multiply both sides by -\frac{45}{2}, the reciprocal of -\frac{2}{45}. Since -\frac{2}{45} is negative, the inequality direction is changed.

$$x>-5\left(-\frac{45}{2}\right)$$

Express -5\left(-\frac{45}{2}\right) as a single fraction.

$$x>\frac{-5\left(-45\right)}{2}$$

Multiply -5 and -45 to get 225.

$$x>\frac{225}{2}$$