Solve the Inequality for b 1/3(15b-12)>=21

$\frac{1}{3} (15 b - 12) \geq 21$

Simplify.

Apply the distributive property.

$\frac{1}{3} (15 b) + \frac{1}{3} \cdot - 12 \geq 21$

Cancel the common factor of $3$ .

Factor $3$ out of $15 b$ .

$\frac{1}{3} (3 (5 b)) + \frac{1}{3} \cdot - 12 \geq 21$

Cancel the common factor.

$\frac{1}{3} (3 (5 b)) + \frac{1}{3} \cdot - 12 \geq 21$

Rewrite the expression.

$5 b + \frac{1}{3} \cdot - 12 \geq 21$

Cancel the common factor of $3$ .

Factor $3$ out of $- 12$ .

$5 b + \frac{1}{3} \cdot (3 (- 4)) \geq 21$

Cancel the common factor.

$5 b + \frac{1}{3} \cdot (3 \cdot - 4) \geq 21$

Rewrite the expression.

$5 b - 4 \geq 21$

Multiply each term in $5 b - 4 \geq 21$ by $3$ to eliminate the fractions.

Multiply each term in $5 b - 4 \geq 21$ by $3$ .

$5 b \cdot 3 - 4 \cdot 3 \geq 21 \cdot 3$

Simplify the left side.

Simplify each term.

Multiply $3$ by $5$ .

$15 b - 4 \cdot 3 \geq 21 \cdot 3$

Multiply $- 4$ by $3$ .

$15 b - 12 \geq 21 \cdot 3$

Simplify the right side.

Multiply $21$ by $3$ .

$15 b - 12 \geq 63$

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

Add $12$ to both sides of the inequality.

$15 b \geq 63 + 12$

Add $63$ and $12$ .

$15 b \geq 75$

Divide each term in $15 b \geq 75$ by $15$ and simplify.

Divide each term in $15 b \geq 75$ by $15$ .

$\frac{15 b}{15} \geq \frac{75}{15}$

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{15 b}{15} \geq \frac{75}{15}$

Divide $b$ by $1$ .

$b \geq \frac{75}{15}$

Simplify the right side.

Divide $75$ by $15$ .

$b \geq 5$

The result can be shown in multiple forms.

Inequality Form:

$b \geq 5$

Interval Notation:

$[5, \infty)$

Solve the Inequality for b 1/3(15b-12)>=21

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