Answer:
[tex]12 > x[/tex]
Step-by-step explanation:
Given: [tex]\frac{1}{3} x + 10 > \frac{3}{4}x + 5[/tex]
Alright, let's start by taking care of those annoying constants 10 and 5. We will start by subtracting 5 from both sides so we are only left with one constant:
[tex]\frac{1}{3} x + 5 > \frac{3}{4}x[/tex]
Now that looks better! Now we need to focus on [tex]x[/tex]. We want both
[tex]5 > \frac{3}{4}x - \frac{1}{3} x[/tex]
Now we have to find a way to have only one [tex]x[/tex]. We can do this by finding a common denominator for both of them. In this case, 12 is our best bet. So for [tex]-\frac{1}{3}x[/tex], we will multiply it by 4 to get 12 in the denominator. For [tex]\frac{1}{4}x[/tex], we shall multiply it by 3. This leaves us with:
[tex]5 > \frac{9}{12}x - \frac{4}{12} x[/tex]
We can also write this as:
[tex]5 > \frac{9x}{12} - \frac{4x}{12}[/tex]
[tex]5 > \frac{9x - 4x}{12}[/tex]
as they are equivalent.
Now we can get our single [tex]x[/tex] variable!
[tex]5 > \frac{5x}{12}[/tex]
And now, we just have to completely isolate it. We need to start with the 12 in the denominator. To do this, we will just multiply both sides by 12.
[tex]60 > 5x[/tex]
And finally, divide both sides by 5.
[tex]12 > x[/tex]
There we have it, our nice and isolated [tex]x[/tex] term.
Hope this helps!
