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

1 Answer
Jun 11, 2015

Answer:

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