Solve for x -2<(4x-1)/3<=0

$- 2 < \frac{4 x - 1}{3} \leq 0$

Step 1

Multiply each term in the inequality by $3$ .

$- 2 \cdot 3 < \frac{4 x - 1}{3} \cdot 3 \leq 0 \cdot 3$

Step 2

Multiply $- 2$ by $3$ .

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

Step 3

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$- 6 < 4 x - 1 \leq 0 \cdot 3$

Step 4

Multiply $0$ by $3$ .

$- 6 < 4 x - 1 \leq 0$

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.

$- 6 + 1 < 4 x \leq 0 + 1$

Add $- 6$ and $1$ .

$- 5 < 4 x \leq 0 + 1$

Add $0$ and $1$ .

$- 5 < 4 x \leq 1$

Step 6

Divide each term in the inequality by $4$ .

$\frac{- 5}{4} < \frac{4 x}{4} \leq \frac{1}{4}$

Step 7

Move the negative in front of the fraction.

$- \frac{5}{4} < \frac{4 x}{4} \leq \frac{1}{4}$

Step 8

Cancel the common factor of $4$ .

Cancel the common factor.

$- \frac{5}{4} < \frac{4 x}{4} \leq \frac{1}{4}$

Divide $x$ by $1$ .

$- \frac{5}{4} < x \leq \frac{1}{4}$

Step 9

The result can be shown in multiple forms.

Inequality Form:

$- \frac{5}{4} < x \leq \frac{1}{4}$

Interval Notation:

$(- \frac{5}{4}, \frac{1}{4}]$

Step 10