Solve for d -5<2d-1<3

$- 5 < 2 d - 1 < 3$

Step 1

Move all terms not containing $d$ 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.

$- 5 + 1 < 2 d < 3 + 1$

Add $- 5$ and $1$ .

$- 4 < 2 d < 3 + 1$

Add $3$ and $1$ .

$- 4 < 2 d < 4$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 4}{2} < \frac{2 d}{2} < \frac{4}{2}$

Step 3

Divide $- 4$ by $2$ .

$- 2 < \frac{2 d}{2} < \frac{4}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- 2 < \frac{2 d}{2} < \frac{4}{2}$

Divide $d$ by $1$ .

$- 2 < d < \frac{4}{2}$

Step 5

Divide $4$ by $2$ .

$- 2 < d < 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 2 < d < 2$

Interval Notation:

$(- 2, 2)$

Step 7