# How do you solve (b-7)/4=(b+9)/7?

Apr 21, 2018

$\frac{85}{3}$

#### Explanation:

Common denominator: LCM of 4 and 7 is 28, or $4 \times 7$
Therefore, we can rewrite the equation as the following:
$\frac{7 \left(b - 7\right)}{28} = \frac{4 \left(b + 9\right)}{28}$ which simplifies to $\frac{7 b - 49}{28} = \frac{4 b + 36}{28}$

Now let's separate the variables. Rewrite again:
$\frac{7 b}{28} - \frac{49}{28} = \frac{4 b}{28} + \frac{36}{28}$

Put the like terms with each other.
$\frac{7 b}{28} - \frac{4 b}{28} = \frac{49}{28} + \frac{36}{28}$

Take out the denominator since they're all equivalent anyway.
$7 b - 4 b = 49 + 36$
Simplify: $3 b = 85$

Divide to isolate variable: $b = \frac{85}{3}$