Solve the Inequality for b -5(2-b)<=7(b+2)

$- 5 (2 - b) \leq 7 (b + 2)$

Step 1

Simplify $- 5 (2 - b)$ .

Start simplifying.

$0 + 0 - 5 (2 - b) \leq 7 (b + 2)$

Simplify by adding zeros.

$- 5 (2 - b) \leq 7 (b + 2)$

Apply the distributive property.

$- 5 \cdot 2 - 5 (- b) \leq 7 (b + 2)$

Multiply.

Multiply $- 5$ by $2$ .

$- 10 - 5 (- b) \leq 7 (b + 2)$

Multiply $- 1$ by $- 5$ .

$- 10 + 5 b \leq 7 (b + 2)$

Step 2

Simplify $7 (b + 2)$ .

Apply the distributive property.

$- 10 + 5 b \leq 7 b + 7 \cdot 2$

Multiply $7$ by $2$ .

$- 10 + 5 b \leq 7 b + 14$

Step 3

Move all terms containing $b$ to the left side of the inequality.

Subtract $7 b$ from both sides of the inequality.

$- 10 + 5 b - 7 b \leq 14$

Subtract $7 b$ from $5 b$ .

$- 10 - 2 b \leq 14$

Step 4

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

Add $10$ to both sides of the inequality.

$- 2 b \leq 14 + 10$

Add $14$ and $10$ .

$- 2 b \leq 24$

Step 5

Divide each term in $- 2 b \leq 24$ by $- 2$ and simplify.

Divide each term in $- 2 b \leq 24$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 b}{- 2} \geq \frac{24}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 b}{- 2} \geq \frac{24}{- 2}$

Divide $b$ by $1$ .

$b \geq \frac{24}{- 2}$

Simplify the right side.

Divide $24$ by $- 2$ .

$b \geq - 12$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$b \geq - 12$

Interval Notation:

$[- 12, \infty)$

Solve the Inequality for b -5(2-b)<=7(b+2)

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