Solve the Inequality for b 8<=4-2b<10

$8 \leq 4 - 2 b < 10$

Step 1

Move all terms not containing $b$ from the center section of the inequality.

Subtract $4$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$8 - 4 \leq - 2 b < 10 - 4$

Subtract $4$ from $8$ .

$4 \leq - 2 b < 10 - 4$

Subtract $4$ from $10$ .

$4 \leq - 2 b < 6$

Step 2

Divide each term in the inequality by $- 2$ .

$\frac{4}{- 2} \geq \frac{- 2 b}{- 2} > \frac{6}{- 2}$

Step 3

Divide $4$ by $- 2$ .

$- 2 \geq \frac{- 2 b}{- 2} > \frac{6}{- 2}$

Step 4

Cancel the common factor of $- 2$ .

Cancel the common factor.

$- 2 \geq \frac{- 2 b}{- 2} > \frac{6}{- 2}$

Divide $b$ by $1$ .

$- 2 \geq b > \frac{6}{- 2}$

Step 5

Divide $6$ by $- 2$ .

$- 2 \geq b > - 3$

Step 6

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

$- 3 < b \leq - 2$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 3 < b \leq - 2$

Interval Notation:

$(- 3, - 2]$

Step 8