# How do you solve (4x-3)/(6-7x)+18=-3?

Aug 6, 2016

$x = \frac{123}{143}$

#### Explanation:

$\frac{4 x - 3}{6 - 7 x} + 18 = - 3$

$\frac{4 x - 3}{6 - 7 x} = - 3 - 18$

$\frac{4 x - 3}{6 - 7 x} = \frac{- 21}{1} \text{ cross multiply}$

$- 21 \left(6 - 7 x\right) = 4 x - 3$

$- 126 + 147 x = 4 x - 3$

$143 x = - 3 + 126$

$143 x = 123$

$x = \frac{123}{143}$

Sep 4, 2016

$x = \frac{123}{143}$

#### Explanation:

We have: $\frac{4 x - 3}{6 - 7 x} + 18 = - 3$

First, let's subtract $18$ from both sides of the equation:

$\implies \frac{4 x - 3}{6 - 7 x} = - 21$

Then. let's multiply both sides by $6 - 7 x$:

$\implies 4 x - 3 = - 21 \left(6 - 7 x\right)$

$\implies 4 x - 3 = - 126 + 147 x$

Let's collect the terms containing $x$ on one side:

$\implies 143 x = 123$

Finally, let's solve for $x$ by dividing both sides by $143$:

$\implies x = \frac{123}{143}$