Solve for x -6<(3x-1)/4<0

$- 6 < \frac{3 x - 1}{4} < 0$

Multiply each term in the inequality by $4$ .

$- 6 \cdot 4 < \frac{3 x - 1}{4} \cdot 4 < 0 \cdot 4$

Multiply $- 6$ by $4$ .

$- 24 < \frac{3 x - 1}{4} \cdot 4 < 0 \cdot 4$

Cancel the common factor of $4$ .

Cancel the common factor.

$- 24 < \frac{3 x - 1}{4} \cdot 4 < 0 \cdot 4$

Rewrite the expression.

$- 24 < 3 x - 1 < 0 \cdot 4$

Multiply $0$ by $4$ .

$- 24 < 3 x - 1 < 0$

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.

$- 24 + 1 < 3 x < 0 + 1$

Add $- 24$ and $1$ .

$- 23 < 3 x < 0 + 1$

Add $0$ and $1$ .

$- 23 < 3 x < 1$

Divide each term in the inequality by $3$ .

$\frac{- 23}{3} < \frac{3 x}{3} < \frac{1}{3}$

Move the negative in front of the fraction.

$- \frac{23}{3} < \frac{3 x}{3} < \frac{1}{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$- \frac{23}{3} < \frac{3 x}{3} < \frac{1}{3}$

Divide $x$ by $1$ .

$- \frac{23}{3} < x < \frac{1}{3}$

The result can be shown in multiple forms.

Inequality Form:

$- \frac{23}{3} < x < \frac{1}{3}$

Interval Notation:

$(- \frac{23}{3}, \frac{1}{3})$