Question

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

Answer 1

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 `(x+4)/(x+4)`, and the second fraction by`(2x-3)/(2x-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(x+4) < 2x-3`

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

`4x+16 < 2x-3`

`2x + 16 < -3`

`2x < -19`

`x < -9.5`

Final Answer