Question

solve for b.
$4 = \frac{2}{3} - \frac{9}{b}$
simplify your answer as much as possible.
$b = \square$

Explanation:

Step1: Isolate the term with $b$

Subtract $\frac{2}{3}$ from both sides.
$$4 - \frac{2}{3} = -\frac{9}{b}$$

Step2: Simplify left-hand side

Calculate the difference of the fractions.
$$\frac{12}{3} - \frac{2}{3} = \frac{10}{3} = -\frac{9}{b}$$

Step3: Cross-multiply to solve for $b$

Multiply both sides by $b$ and $\frac{3}{10}$.
$$b = -\frac{9 \times 3}{10}$$

Step4: Compute final value

Calculate the numerator.
$$b = -\frac{27}{10}$$

Answer:

$b = -\frac{27}{10}$