We are asked to find a range for x. Let's start by finding the maximum value. We know, by definition, that a side opposite a larger angle has a longer length. For example, if you think about a right triangle, the hypotenuse (the longest side) is always opposite of the right angle (the largest angle). We are given two side lengths: 23 is opposite of 42 degrees, and 21 is opposite of 3x + 15. Because 42 is opposite the longer side, 42 degrees is a larger angle than 3x + 15. We can set up the inequality and solve for x:

Now, let's look at the minimum value. We know that the angle definitely has to be larger than 0. So, we can set up that inequality and solve for x:

Now, we have our final range: -5 < x < 9
I should be on the black dot ☺️
<em>The answer is 10:7, 10/7, 10 to 7. Whichever it's asking for. As long as you know the ratio is 10 rock songs to 7 country songs.
</em><em /><u>
</u><em />This problem can be a simple fraction simplification problem. Here's what I mean:
<em>
</em><em />So, we have 40 rock songs and 28 country songs. Let's put that into a fraction:
<em>
</em>
<em>
</em>To simplify this as much as possible, all we have to do is find the greatest common multiple and divide it by both numbers. the GCF is 4, so all you have to do is divide 40 by 4 and 28 by 4 to get your ratios.
<em>
I hope this helped!!
</em>