Solve for x -7<(2x-1)/2<0

$- 7 < \frac{2 x - 1}{2} < 0$

Step 1

Multiply each term in the inequality by $2$ .

$- 7 \cdot 2 < \frac{2 x - 1}{2} \cdot 2 < 0 \cdot 2$

Step 2

Multiply $- 7$ by $2$ .

$- 14 < \frac{2 x - 1}{2} \cdot 2 < 0 \cdot 2$

Step 3

Cancel the common factor of $2$ .

Cancel the common factor.

$- 14 < \frac{2 x - 1}{2} \cdot 2 < 0 \cdot 2$

Rewrite the expression.

$- 14 < 2 x - 1 < 0 \cdot 2$

Step 4

Multiply $0$ by $2$ .

$- 14 < 2 x - 1 < 0$

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.

$- 14 + 1 < 2 x < 0 + 1$

Add $- 14$ and $1$ .

$- 13 < 2 x < 0 + 1$

Add $0$ and $1$ .

$- 13 < 2 x < 1$

Step 6

Divide each term in the inequality by $2$ .

$\frac{- 13}{2} < \frac{2 x}{2} < \frac{1}{2}$

Step 7

Move the negative in front of the fraction.

$- \frac{13}{2} < \frac{2 x}{2} < \frac{1}{2}$

Step 8

Cancel the common factor of $2$ .

Cancel the common factor.

$- \frac{13}{2} < \frac{2 x}{2} < \frac{1}{2}$

Divide $x$ by $1$ .

$- \frac{13}{2} < x < \frac{1}{2}$

Step 9

The result can be shown in multiple forms.

Inequality Form:

$- \frac{13}{2} < x < \frac{1}{2}$

Interval Notation:

$(- \frac{13}{2}, \frac{1}{2})$

Step 10