Solve for x -7<(5x-1)/4<0

$- 7 < \frac{5 x - 1}{4} < 0$

Step 1

Multiply each term in the inequality by $4$ .

$- 7 \cdot 4 < \frac{5 x - 1}{4} \cdot 4 < 0 \cdot 4$

Step 2

Multiply $- 7$ by $4$ .

$- 28 < \frac{5 x - 1}{4} \cdot 4 < 0 \cdot 4$

Step 3

Cancel the common factor of $4$ .

Cancel the common factor.

$- 28 < \frac{5 x - 1}{4} \cdot 4 < 0 \cdot 4$

Rewrite the expression.

$- 28 < 5 x - 1 < 0 \cdot 4$

Step 4

Multiply $0$ by $4$ .

$- 28 < 5 x - 1 < 0$

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.

$- 28 + 1 < 5 x < 0 + 1$

Add $- 28$ and $1$ .

$- 27 < 5 x < 0 + 1$

Add $0$ and $1$ .

$- 27 < 5 x < 1$

Step 6

Divide each term in the inequality by $5$ .

$\frac{- 27}{5} < \frac{5 x}{5} < \frac{1}{5}$

Step 7

Move the negative in front of the fraction.

$- \frac{27}{5} < \frac{5 x}{5} < \frac{1}{5}$

Step 8

Cancel the common factor of $5$ .

Cancel the common factor.

$- \frac{27}{5} < \frac{5 x}{5} < \frac{1}{5}$

Divide $x$ by $1$ .

$- \frac{27}{5} < x < \frac{1}{5}$

Step 9

The result can be shown in multiple forms.

Inequality Form:

$- \frac{27}{5} < x < \frac{1}{5}$

Interval Notation:

$(- \frac{27}{5}, \frac{1}{5})$

Step 10