Solve x/2<5x-2/3-7x-3/5

$$\frac { x } { 2 } < \frac { 5 x - 2 } { 3 } - \frac { 7 x - 3 } { 5 }$$

Solve for x

$$x<-\frac{2}{7}$$

Solution Steps

Multiply both sides of the equation by 30, the least common multiple of 2,3,5. Since 30 is positive, the inequality direction remains the same.

$$15x<10\left(5x-2\right)-6\left(7x-3\right)$$

Use the distributive property to multiply 10 by 5x-2.

$$15x<50x-20-6\left(7x-3\right)$$

Use the distributive property to multiply -6 by 7x-3.

$$15x<50x-20-42x+18$$

Combine 50x and -42x to get 8x.

$$15x<8x-20+18$$

Add -20 and 18 to get -2.

$$15x<8x-2$$

Subtract 8x from both sides.

$$15x-8x<-2$$

Combine 15x and -8x to get 7x.

$$7x<-2$$

Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.

$$x<-\frac{2}{7}$$