Solve x+1/3<x/2-1

$$\frac{ x+1 }{ 3 } < \frac{ x }{ 2 } -1$$

Solve for x

$$x>8$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

$$2\left(x+1\right)<3x-6$$

Use the distributive property to multiply 2 by x+1.

$$2x+2<3x-6$$

Subtract 3x from both sides.

$$2x+2-3x<-6$$

Combine 2x and -3x to get -x.

$$-x+2<-6$$

Subtract 2 from both sides.

$$-x<-6-2$$

Subtract 2 from -6 to get -8.

$$-x<-8$$

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

$$x>\frac{-8}{-1}$$

Fraction \frac{-8}{-1} can be simplified to 8 by removing the negative sign from both the numerator and the denominator.

$$x>8$$