Solve the Inequality for b b+12/7>=1/3

$b + \frac{12}{7} \geq \frac{1}{3}$

Subtract $\frac{12}{7}$ from both sides of the inequality.

$b \geq \frac{1}{3} - \frac{12}{7}$

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$b \geq \frac{1}{3} \cdot \frac{7}{7} - \frac{12}{7}$

To write $- \frac{12}{7}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$b \geq \frac{1}{3} \cdot \frac{7}{7} - \frac{12}{7} \cdot \frac{3}{3}$

Write each expression with a common denominator of $21$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{3}$ by $\frac{7}{7}$ .

$b \geq \frac{7}{3 \cdot 7} - \frac{12}{7} \cdot \frac{3}{3}$

Multiply $3$ by $7$ .

$b \geq \frac{7}{21} - \frac{12}{7} \cdot \frac{3}{3}$

Multiply $\frac{12}{7}$ by $\frac{3}{3}$ .

$b \geq \frac{7}{21} - \frac{12 \cdot 3}{7 \cdot 3}$

Multiply $7$ by $3$ .

$b \geq \frac{7}{21} - \frac{12 \cdot 3}{21}$

Combine the numerators over the common denominator.

$b \geq \frac{7 - 12 \cdot 3}{21}$

Simplify the numerator.

Multiply $- 12$ by $3$ .

$b \geq \frac{7 - 36}{21}$

Subtract $36$ from $7$ .

$b \geq \frac{- 29}{21}$

Move the negative in front of the fraction.

$b \geq - \frac{29}{21}$

The result can be shown in multiple forms.

Inequality Form:

$b \geq - \frac{29}{21}$

Interval Notation:

$[- \frac{29}{21}, \infty)$