Lösung 2.2:2a
Aus Online Mathematik Brückenkurs 1
If we divide up the denominators that appear in the equation into small integer factors \displaystyle 6=2\cdot 3, \displaystyle 9=3\cdot 3 and 2, we see that the lowest common denominator is \displaystyle 2\cdot 3\cdot 3=18. Thus, we multiply both sides of the equation by \displaystyle 2\cdot 3\cdot 3 in order to avoid having denominators in the equation
We can rewrite the left-hand side as \displaystyle 3\cdot 5x-2\cdot (x+2) = 15x-2x-4 = 13x-4, so that we get the equation
We can now solve this first-degree equation by carrying out simple arithmetical calculations so as to get x by itself on one side:
- Add 4 to both sides, \displaystyle \vphantom{x_2}13x-4+4=9+4\,, which gives \displaystyle \ 13x=13\,\textrm{.}
- Divide both sides by 13, \displaystyle \frac{13x}{13}=\frac{13}{13}\,, which gives the answer \displaystyle \ x=1\,\textrm{.}
The equation has \displaystyle x=1 as the solution.
When we have obtained an answer, it is important to go back to the original equation to check that \displaystyle x=1 really is the correct answer (i.e. that we haven't calculated incorrectly)
