# How do you solve and graph the inequality (4)/(2x-3) < (1)/(x+4)?

Jun 11, 2015

By finding a common denominator, and then using equality properties. Spoiler: $x < - 9.5$

#### Explanation:

With these kinds of questions, a one sentence answer won't work. Here's how this equation is solved:

We first need to get the 2 fractions to have the same denominator. Let's multiply the first fraction by $\frac{x + 4}{x + 4}$, and the second fraction by$\frac{2 x - 3}{2 x - 3}$. This gives us:

(4(x+4))/((2x−3)(x+4)) < (2x-3)/((2x-3)(x+4))

Now, we can multiply both sides by (2x-3) and (x+4) to get rid of the denominators.

$4 \left(x + 4\right) < 2 x - 3$

That's much simpler, isn't it? Now it's easy to simplify and solve this.

$4 x + 16 < 2 x - 3$

$2 x + 16 < - 3$

$2 x < - 19$

$x < - 9.5$