Solve 2(x-4)/6-3x>3(x-1)

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

Solve for x

$$x<\frac{5}{17}$$

Solution Steps

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

$$2\left(x-4\right)-18x>18\left(x-1\right)$$

Use the distributive property to multiply 2 by x-4.

$$2x-8-18x>18\left(x-1\right)$$

Combine 2x and -18x to get -16x.

$$-16x-8>18\left(x-1\right)$$

Use the distributive property to multiply 18 by x-1.

$$-16x-8>18x-18$$

Subtract 18x from both sides.

$$-16x-8-18x>-18$$

Combine -16x and -18x to get -34x.

$$-34x-8>-18$$

Add 8 to both sides.

$$-34x>-18+8$$

Add -18 and 8 to get -10.

$$-34x>-10$$

Divide both sides by -34. Since -34 is negative, the inequality direction is changed.

$$x<\frac{-10}{-34}$$

Reduce the fraction \frac{-10}{-34} to lowest terms by extracting and canceling out -2.

$$x<\frac{5}{17}$$