Solve the Inequality for b 30b+53>=18b-83

$30 b + 53 \geq 18 b - 83$

Step 1

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

Subtract $18 b$ from both sides of the inequality.

$30 b + 53 - 18 b \geq - 83$

Subtract $18 b$ from $30 b$ .

$12 b + 53 \geq - 83$

Step 2

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

Subtract $53$ from both sides of the inequality.

$12 b \geq - 83 - 53$

Subtract $53$ from $- 83$ .

$12 b \geq - 136$

Step 3

Divide each term in $12 b \geq - 136$ by $12$ and simplify.

Divide each term in $12 b \geq - 136$ by $12$ .

$\frac{12 b}{12} \geq \frac{- 136}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 b}{12} \geq \frac{- 136}{12}$

Divide $b$ by $1$ .

$b \geq \frac{- 136}{12}$

Simplify the right side.

Cancel the common factor of $- 136$ and $12$ .

Factor $4$ out of $- 136$ .

$b \geq \frac{4 (- 34)}{12}$

Cancel the common factors.

Factor $4$ out of $12$ .

$b \geq \frac{4 \cdot - 34}{4 \cdot 3}$

Cancel the common factor.

$b \geq \frac{4 \cdot - 34}{4 \cdot 3}$

Rewrite the expression.

$b \geq \frac{- 34}{3}$

Move the negative in front of the fraction.

$b \geq - \frac{34}{3}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$b \geq - \frac{34}{3}$

Interval Notation:

$[- \frac{34}{3}, \infty)$