Solve the Inequality for b 3(6b-1)>18-3b

$3 (6 b - 1) > 18 - 3 b$

Step 1

Simplify $3 (6 b - 1)$ .

Rewrite.

$0 + 0 + 3 (6 b - 1) > 18 - 3 b$

Simplify by adding zeros.

$3 (6 b - 1) > 18 - 3 b$

Apply the distributive property.

$3 (6 b) + 3 \cdot - 1 > 18 - 3 b$

Multiply.

Multiply $6$ by $3$ .

$18 b + 3 \cdot - 1 > 18 - 3 b$

Multiply $3$ by $- 1$ .

$18 b - 3 > 18 - 3 b$

Step 2

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

Add $3 b$ to both sides of the inequality.

$18 b - 3 + 3 b > 18$

Add $18 b$ and $3 b$ .

$21 b - 3 > 18$

Step 3

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

Add $3$ to both sides of the inequality.

$21 b > 18 + 3$

Add $18$ and $3$ .

$21 b > 21$

Step 4

Divide each term in $21 b > 21$ by $21$ and simplify.

Divide each term in $21 b > 21$ by $21$ .

$\frac{21 b}{21} > \frac{21}{21}$

Simplify the left side.

Cancel the common factor of $21$ .

Cancel the common factor.

$\frac{21 b}{21} > \frac{21}{21}$

Divide $b$ by $1$ .

$b > \frac{21}{21}$

Simplify the right side.

Divide $21$ by $21$ .

$b > 1$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$b > 1$

Interval Notation:

$(1, \infty)$