Solve 8+x/12<x-1/10

$$\frac { 8 + x } { 12 } < \frac { x - 1 } { 10 }$$

Solve for x

$$x>46$$

Solution Steps

Multiply both sides of the equation by 60, the least common multiple of 12,10. Since 60 is positive, the inequality direction remains the same.

$$5\left(8+x\right)<6\left(x-1\right)$$

Use the distributive property to multiply 5 by 8+x.

$$40+5x<6\left(x-1\right)$$

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

$$40+5x<6x-6$$

Subtract 6x from both sides.

$$40+5x-6x<-6$$

Combine 5x and -6x to get -x.

$$40-x<-6$$

Subtract 40 from both sides.

$$-x<-6-40$$

Subtract 40 from -6 to get -46.

$$-x<-46$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x>\frac{-46}{-1}$$

Fraction \frac{-46}{-1} can be simplified to 46 by removing the negative sign from both the numerator and the denominator.

$$x>46$$