Solve for x -6<(3x-1)/2<0

$- 6 < \frac{3 x - 1}{2} < 0$

Step 1

Multiply each term in the inequality by $2$ .

$- 6 \cdot 2 < \frac{3 x - 1}{2} \cdot 2 < 0 \cdot 2$

Step 2

Multiply $- 6$ by $2$ .

$- 12 < \frac{3 x - 1}{2} \cdot 2 < 0 \cdot 2$

Step 3

Cancel the common factor of $2$ .

Cancel the common factor.

$- 12 < \frac{3 x - 1}{2} \cdot 2 < 0 \cdot 2$

Rewrite the expression.

$- 12 < 3 x - 1 < 0 \cdot 2$

Step 4

Multiply $0$ by $2$ .

$- 12 < 3 x - 1 < 0$

Step 5

Move all terms not containing $x$ from the center section of the inequality.

Add $1$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 12 + 1 < 3 x < 0 + 1$

Add $- 12$ and $1$ .

$- 11 < 3 x < 0 + 1$

Add $0$ and $1$ .

$- 11 < 3 x < 1$

Step 6

Divide each term in the inequality by $3$ .

$\frac{- 11}{3} < \frac{3 x}{3} < \frac{1}{3}$

Step 7

Move the negative in front of the fraction.

$- \frac{11}{3} < \frac{3 x}{3} < \frac{1}{3}$

Step 8

Cancel the common factor of $3$ .

Cancel the common factor.

$- \frac{11}{3} < \frac{3 x}{3} < \frac{1}{3}$

Divide $x$ by $1$ .

$- \frac{11}{3} < x < \frac{1}{3}$

Step 9

The result can be shown in multiple forms.

Inequality Form:

$- \frac{11}{3} < x < \frac{1}{3}$

Interval Notation:

$(- \frac{11}{3}, \frac{1}{3})$

Step 10