I know the correct answer is x=-32/19 because my teacher gives us the answers on the back of our worksheet, but when I do the actual work I get x=3
It's so simple, yet I've tried several times and get the same answer. Could anyone explain how to do it?
3/4x-2/3x-4=1/6x-7
+169 $${\frac{{\mathtt{3}}}{{\mathtt{4}}}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\frac{{\mathtt{2}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{4}} = {\frac{{\mathtt{1}}}{{\mathtt{6}}}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{7}}$$
$${\frac{{\mathtt{3}}}{{\mathtt{4}}}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\frac{{\mathtt{2}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{6}}}}{\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{4}}{\mathtt{\,-\,}}{\mathtt{7}}$$
$${\frac{{\mathtt{9}}}{{\mathtt{12}}}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\frac{{\mathtt{8}}}{{\mathtt{12}}}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\frac{{\mathtt{2}}}{{\mathtt{12}}}}{\mathtt{\,\times\,}}{\mathtt{x}} = -{\mathtt{3}}$$
$${\frac{\left({\mathtt{9}}{\mathtt{\,-\,}}{\mathtt{8}}{\mathtt{\,-\,}}{\mathtt{2}}\right)}{{\mathtt{12}}}}{\mathtt{\,\times\,}}{\mathtt{x}} = -{\mathtt{3}}$$
$${\mathtt{\,-\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{12}}}}{\mathtt{\,\times\,}}{\mathtt{x}}\right) = -{\mathtt{3}}$$
$${\mathtt{x}} = {\mathtt{\,-\,}}{\frac{{\mathtt{3}}}{{\mathtt{\,-\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{12}}}}\right)}}$$
$${\mathtt{x}} = {\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{12}} = {\mathtt{36}}$$
You probably gave a wrong equation or the wrong answer, 19 is a prime number and doesn't appear anywhere in the original equation (neither does a multiple of 19). This makes it highy unlikely that a fraction including 19 would be the answer.
