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

Evaluate

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

Multiply both sides of the inequality by 3 \times 2

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

Multiply the terms

More Steps

4 x - 12 - 9 x + 3 > \frac{x}{6} \times 3 \times 2

Multiply the terms

4 x - 12 - 9 x + 3 > x

Calculate the sum or difference

More Steps

- 5 x - 9 > x

Move the variable to the left side

- 5 x - 9 - x > 0

Subtract the terms

More Steps

- 6 x - 9 > 0

Move the constant to the right side

- 6 x > 0 + 9

Removing 0 doesn't change the value,so remove it from the expression

- 6 x > 9

Change the signs on both sides of the inequality and flip the inequality sign

6 x < - 9

Divide both sides

\frac{6 x}{6} < \frac{- 9}{6}

Divide the numbers

x < \frac{- 9}{6}

Solution

More Steps

x < - \frac{3}{2}

Alternative Form

x \in (- \infty, - \frac{3}{2})

Solve the inequality