Solve x+1/3-x-1/5>x/10

$$\frac { x + 1 } { 3 } - \frac { x - 1 } { 5 } > \frac { x } { 10 }$$

Solve for x

$$x>-16$$

Solution Steps

Multiply both sides of the equation by 30, the least common multiple of 3,5,10. Since 30 is positive, the inequality direction remains the same.

$$10\left(x+1\right)-6\left(x-1\right)>3x$$

Use the distributive property to multiply 10 by x+1.

$$10x+10-6\left(x-1\right)>3x$$

Use the distributive property to multiply -6 by x-1.

$$10x+10-6x+6>3x$$

Combine 10x and -6x to get 4x.

$$4x+10+6>3x$$

Add 10 and 6 to get 16.

$$4x+16>3x$$

Subtract 3x from both sides.

$$4x+16-3x>0$$

Combine 4x and -3x to get x.

$$x+16>0$$

Subtract 16 from both sides. Anything subtracted from zero gives its negation.

$$x>-16$$