Solve 2(x+1)/3-2(3x+2)/6<(x-4)/1

$$\frac{ 2(x+1) }{ 3 } - \frac{ 2(3x+2) }{ 6 } < \frac{ (x-4) }{ 1 }$$

Solve for x

$$x>3$$

Solution Steps

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

$$2\times 2\left(x+1\right)-2\left(3x+2\right)<6\left(x-4\right)$$

Multiply 2 and 2 to get 4.

$$4\left(x+1\right)-2\left(3x+2\right)<6\left(x-4\right)$$

Use the distributive property to multiply 4 by x+1.

$$4x+4-2\left(3x+2\right)<6\left(x-4\right)$$

Use the distributive property to multiply -2 by 3x+2.

$$4x+4-6x-4<6\left(x-4\right)$$

Combine 4x and -6x to get -2x.

$$-2x+4-4<6\left(x-4\right)$$

Subtract 4 from 4 to get 0.

$$-2x<6\left(x-4\right)$$

Use the distributive property to multiply 6 by x-4.

$$-2x<6x-24$$

Subtract 6x from both sides.

$$-2x-6x<-24$$

Combine -2x and -6x to get -8x.

$$-8x<-24$$

Divide both sides by -8. Since -8 is negative, the inequality direction is changed.

$$x>\frac{-24}{-8}$$

Divide -24 by -8 to get 3.

$$x>3$$