Solve the Inequality for b 4(8-2b)-2b<=32

$4 (8 - 2 b) - 2 b \leq 32$

Step 1

Simplify $4 (8 - 2 b) - 2 b$ .

Simplify each term.

Apply the distributive property.

$4 \cdot 8 + 4 (- 2 b) - 2 b \leq 32$

Multiply $4$ by $8$ .

$32 + 4 (- 2 b) - 2 b \leq 32$

Multiply $- 2$ by $4$ .

$32 - 8 b - 2 b \leq 32$

Subtract $2 b$ from $- 8 b$ .

$32 - 10 b \leq 32$

Step 2

Move all terms not containing $b$ to the right side of the inequality.

Subtract $32$ from both sides of the inequality.

$- 10 b \leq 32 - 32$

Subtract $32$ from $32$ .

$- 10 b \leq 0$

Step 3

Divide each term in $- 10 b \leq 0$ by $- 10$ and simplify.

Divide each term in $- 10 b \leq 0$ by $- 10$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 10 b}{- 10} \geq \frac{0}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 b}{- 10} \geq \frac{0}{- 10}$

Divide $b$ by $1$ .

$b \geq \frac{0}{- 10}$

Simplify the right side.

Divide $0$ by $- 10$ .

$b \geq 0$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$b \geq 0$

Interval Notation:

$[0, \infty)$

Solve the Inequality for b 4(8-2b)-2b<=32

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